A Discrete-Time Compartmental Epidemiological Model for COVID-19 with a Case Study for Portugal

scientific article published in 2021

A Hukuhara approach to the study of hybrid fuzzy systems on time scales ⬇️

A Numerical Scheme to Solve Fractional Optimal Control Problems

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A SICA compartmental model in epidemiology with application to HIV/AIDS in Cape Verde

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A Simple Accurate Method for Solving Fractional Variational and Optimal Control Problems

A Symmetric Nörlund Sum with Application to Inequalities

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A Symmetric Quantum Calculus

scientific article published in 2013

A TB-HIV/AIDS coinfection model and optimal control treatment ⬇️

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A class of fractional differential equations via power non-local and non-singular kernels: Existence, uniqueness and numerical approximations

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A conformable fractional calculus on arbitrary time scales ⬇️

A discrete method to solve fractional optimal control problems ⬇️

A discrete time method to the first variation of fractional order variational functionals

A formulation of Noether's theorem for fractional problems of the calculus of variations

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A fractional calculus of variations for multiple integrals with application to vibrating string

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A fractional calculus on arbitrary time scales: Fractional differentiation and fractional integration ⬇️

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A general backwards calculus of variations via duality

A general delta-nabla calculus of variations on time scales with application to economics ⬇️

A generalized Lyapunov’s inequality for a fractional boundary value problem ⬇️

scholarly article by Amar Chidouh & Delfim F.M. Torres published March 2017 in Journal of Computational and Applied Mathematics

A necessary condition of Pontryagin type for fuzzy fractional optimal control problems

A necessary optimality condition for extended weighted generalized fractional optimal control problems

scientific article published in March 2024

A non-classical class of variational problems

A simple mathematical model for unemployment: a case study in Portugal with optimal control

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A space–time pseudospectral discretization method for solving diffusion optimal control problems with two-sided fractional derivatives

A stochastic SICA epidemic model for HIV transmission

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A survey on fuzzy fractional differential and optimal control nonlocal evolution equations

scholarly article by Ravi P. Agarwal et al published September 2018 in Journal of Computational and Applied Mathematics

A unified approach to the calculus of variations on time scales

An Optimal Control Approach to Herglotz Variational Problems ⬇️

An Optimal Control Approach to Malaria Prevention via Insecticide-Treated Nets

scholarly article published 2013

An epidemic model for cholera with optimal control treatment ⬇️

scholarly article by Ana P. Lemos-Paião et al published July 2017 in Journal of Computational and Applied Mathematics

An expansion formula with higher-order derivatives for fractional operators of variable order.

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Analysis and Optimal Control of an Intracellular Delayed HIV Model with CTL Immune Response

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Analysis of Hilfer Fractional Integro-Differential Equations with Almost Sectorial Operators

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Analysis of vibrations in large flexible hybrid systems

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Approximate controllability of fractional delay dynamic inclusions with nonlocal control conditions ⬇️

scholarly article by Amar Debbouche & Delfim F.M. Torres published September 2014 in Applied Mathematics and Computation

Approximate controllability of fractional nonlocal delay semilinear systems in Hilbert spaces

Approximated analytical solution to an Ebola optimal control problem ⬇️

Approximation of fractional integrals by means of derivatives

Automatic Computation of Conservation Laws in the Calculus of Variations and Optimal Control

Avoidance Control on Time Scales

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Backward linear control systems on time scales

Banking Risk as an Epidemiological Model: An Optimal Control Approach

scholarly article by Olena Kostylenko et al published 2018 in Springer Proceedings in Mathematics & Statistics

Bioeconomic perspectives to an optimal control dengue model

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Boundary controllability of Riemann–Liouville fractional semilinear equations

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Calculus of variations on time scales with nabla derivatives

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Calculus of variations with fractional derivatives and fractional integrals

Caputo derivatives of fractional variable order: Numerical approximations ⬇️

scholarly article by Dina Tavares et al published June 2016 in Communications in Nonlinear Science and Numerical Simulation

Carathéodory Equivalence, Noether Theorems, and Tonelli Full-Regularity in the Calculus of Variations and Optimal Control

article published in 2004

Cauchy’s formula on nonempty closed sets and a new notion of Riemann–Liouville fractional integral on time scales

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Chain rules and inequalities for the BHT fractional calculus on arbitrary timescales ⬇️

Coexistence of two dengue virus serotypes and forecasting for Madeira Island ⬇️

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Combined dynamic Grüss inequalities on time scales

Combined fractional variational problems of variable order and some computational aspects ⬇️

scholarly article by Dina Tavares et al published September 2018 in Journal of Computational and Applied Mathematics

Comment on “Noether’s-type theorems on time scales” [J. Math. Phys. 61, 113502 (2020)]

scientific article published in 2023

Complex network model for COVID-19: Human behavior, pseudo-periodic solutions and multiple epidemic waves

scientific article published on 23 March 2021

Complex-Valued Fractional Derivatives on Time Scales ⬇️

Computational Approach to Essential and Nonessential Objective Functions in Linear Multicriteria Optimization

Computing Hadamard type operators of variable fractional order ⬇️

scholarly article by Ricardo Almeida & Delfim F.M. Torres published April 2015 in Applied Mathematics and Computation

Computing ODE symmetries as abnormal variational symmetries

Conservation laws for invariant functionals containing compositions§

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Constrained fractional variational problems of variable order ⬇️

article by Dina Tavares et al published January 2017 in IEEE/CAA Journal of Automatica Sinica

Contrasting Two Transformation-based Methods for Obtaining Absolute Extrema

Control of a novel chaotic fractional order system using a state feedback technique

Corrigendum to "Mathematical Modeling of COVID-19 Transmission Dynamics with a Case Study of Wuhan" [Chaos Solitons Fractals 135 (2020), 109846]

scientific article published on 24 September 2020

Cost-effectiveness analysis of optimal control measures for tuberculosis. ⬇️

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Dengue disease, basic reproduction number and control

Dengue in Cape Verde: Vector Control and Vaccination

scholarly article by HELENA SOFIA RODRIGUES et al published October 2013 in Mathematical Population Studies

Dengue in Madeira Island ⬇️

Direct and Inverse Variational Problems on Time Scales: A Survey

Discrete direct methods in the fractional calculus of variations

Discrete-time fractional variational problems

Duality for the left and right fractional derivatives ⬇️

scholarly article by M. Cristina Caputo & Delfim F.M. Torres published February 2015 in Signal Processing

Dynamics and Optimal Control of Ebola Transmission ⬇️

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Dynamics of Dengue epidemics when using optimal control

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Dynamics of a model of polluted lakes via fractal–fractional operators with two different numerical algorithms

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Dynamics of controlled hybrid systems of aerial cable-ways

Ebola model and optimal control with vaccination constraints

Enhancement of chemotherapy using oncolytic virotherapy: Mathematical and optimal control analysis

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Enlarged Controllability of Riemann–Liouville Fractional Differential Equations

Euler-Lagrange equations for composition functionals in calculus of variations on time scales

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Existence Results for a Multipoint Fractional Boundary Value Problem in the Fractional Derivative Banach Space

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Existence and Uniqueness of Weak Solutions to Frictionless-Antiplane Contact Problems

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Existence and uniqueness of solution for a fractional Riemann–Liouville initial value problem on time scales ⬇️

Existence and uniqueness of solution for fractional differential equations with integral boundary conditions and the Adomian decomposition method

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Existence and uniqueness results for a fractional Riemann–Liouville nonlocal thermistor problem on arbitrary time scales ⬇️

Existence of Three Positive Solutions to Somep-Laplacian Boundary Value Problems

Existence of positive solutions to a discrete fractional boundary value problem and corresponding Lyapunov-type inequalities

Existence of solution to a local fractional nonlinear differential equation ⬇️

scholarly article by Benaoumeur Bayour & Delfim F.M. Torres published March 2017 in Journal of Computational and Applied Mathematics

Existence theorems for a nonlinear second-order distributional differential equation

Expansion Formulas for Fractional Derivatives

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Expansion Formulas in Terms of Integer-Order Derivatives for the Hadamard Fractional Integral and Derivative

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Exponentials and Laplace transforms on nonuniform time scales ⬇️

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Fractional Calculus

Fractional Calculus of Variations in Terms of a Generalized Fractional Integral with Applications to Physics

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Fractional Derivatives in Dengue Epidemics

Fractional Euler–Lagrange Differential Equations via Caputo Derivatives

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Fractional Herglotz variational principles with generalized Caputo derivatives ⬇️

Fractional Herglotz variational problems of variable order

Fractional Isoperimetric Noether's Theorem in the Riemann–Liouville Sense

Fractional Modelling and Optimal Control of COVID-19 Transmission in Portugal

scientific article published in 2022

Fractional Noether's theorem with classical and Riemann-Liouville derivatives

Fractional Noether’s theorem in the Riesz–Caputo sense

Fractional actionlike variational problems

Fractional and Time-Scales Differential Equations

Fractional calculus of variations for a combined Caputo derivative

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Fractional conservation laws in optimal control theory

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Fractional h-difference equations arising from the calculus of variations

Fractional order optimal control problems with free terminal time

Fractional variational calculus for nondifferentiable functions

Fractional variational calculus with classical and combined Caputo derivatives

Fractional variational problems depending on indefinite integrals

Galerkin spectral method for the fractional nonlocal thermistor problem ⬇️

General fractional-order anomalous diffusion with non-singular power-law kernel

Generalizations of Gronwall–Bihari inequalities on time scales

Generalized Euler–Lagrange Equations for Variational Problems with Scale Derivatives

Generalized fractional calculus with applications to the calculus of variations

Generalized fractional operators for nonstandard Lagrangians ⬇️

Generalized fractional operators on time scales with application to dynamic equations

Generalized natural boundary conditions for fractional variational problems in terms of the Caputo derivative

Generalized retarded integral inequalities

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Generalized weighted Ostrowski and Ostrowski-Grüss type inequalities on time scales via a parameter function

Generalizing the variational theory on time scales to include the delta indefinite integral

Global existence of solutions for a fractional Caputo nonlocal thermistor problem

Green’s theorem for generalized fractional derivatives

Hahn's symmetric quantum variational calculus

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Helmholtz Theorem for Nondifferentiable Hamiltonian Systems in the Framework of Cresson’s Quantum Calculus ⬇️

Higher-Order Calculus of Variations on Time Scales

Higher-Order Variational Problems of Herglotz Type

Higher-order Hahn’s quantum variational calculus

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Higher-order infinite horizon variational problems in discrete quantum calculus

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Hybrid Method for Simulation of a Fractional COVID-19 Model with Real Case Application

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Hyperchaotic Fractional-Order Systems and Their Applications

Hölderian variational problems subject to integral constraints

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Insecticide Control in a Dengue Epidemics Model

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Introduction to the Fractional Calculus of Variations

Isoperimetric Problems on Time Scales with Nabla Derivatives

Isoperimetric problems of the calculus of variations with fractional derivatives

Leitmann’s direct method for fractional optimization problems

Leitmann’s direct method of optimization for absolute extrema of certain problems of the calculus of variations on time scales

Linear and Nonlinear Fractional Voigt Models ⬇️

Lipschitzian Regularity of Minimizers for Optimal Control Problems with Control-Affine Dynamics

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Lipschitzian Regularity of the Minimizing Trajectories for Nonlinear Optimal Control Problems

Lyapunov-type inequality for a fractional boundary value problem with natural conditions ⬇️

Mathematical Analysis of a Fractional COVID-19 Model Applied to Wuhan, Spain and Portugal

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Mathematical Modeling and Control of Infectious Diseases.

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Mathematical Modeling of COVID-19 Transmission Dynamics with a Case Study of Wuhan

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Mathematical Modelling, Simulation, and Optimal Control of the 2014 Ebola Outbreak in West Africa ⬇️

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Mathematical modeling of Zika disease in pregnant women and newborns with microcephaly in Brazil

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Minimum Energy Problem in the Sense of Caputo for Fractional Neutral Evolution Systems in Banach Spaces

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Modeling TB-HIV Syndemic and Treatment ⬇️

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Modeling and Forecasting of COVID-19 Spreading by Delayed Stochastic Differential Equations

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Modeling and optimal control of HIV/AIDS prevention through PrEP

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Modeling blood alcohol concentration using fractional differential equations based on the ψ‐Caputo derivative

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Modeling the dynamics of the Hepatitis B virus via a variable-order discrete system

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Modified optimal energy and initial memory of fractional continuous-time linear systems

Multiobjective approach to optimal control for a dengue transmission model ⬇️

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Multiobjective approach to optimal control for a tuberculosis model ⬇️

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Multiobjective fractional variational calculus in terms of a combined Caputo derivative

Multiobjective optimization to a TB-HIV/AIDS coinfection optimal control problem ⬇️

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Nabla Fractional Derivative and Fractional Integral on Time Scales

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Natural boundary conditions in the calculus of variations

Necessary Condition for an Euler-Lagrange Equation on Time Scales ⬇️

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Necessary Optimality Condition for a Discrete Dead Oil Isotherm Optimal Control Problem

Necessary Optimality Conditions for Higher-Order Infinite Horizon Variational Problems on Time Scales

Necessary Optimality Conditions for a Dead Oil Isotherm Optimal Control Problem

Necessary and sufficient conditions for local Pareto optimality on time scales

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Necessary and sufficient conditions for the fractional calculus of variations with Caputo derivatives

Necessary optimality conditions for fractional action-like integrals of variational calculus with Riemann–Liouville derivatives of order (α, β)

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Necessary optimality conditions for fractional difference problems of the calculus of variations

Necessary optimality conditions for infinite horizon variational problems on time scales

Newton's aerodynamic problem in media of chaotically moving particles

Noether currents for higher-order variational problems of Herglotz type with time delay

Noether's symmetry Theorem for variational and optimal control problems with time delay

Noether's theorem for higher-order variational problems of Herglotz type ⬇️

Noether's theorem on time scales

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Noether’s symmetry theorem for nabla problems of the calculus of variations

Noether’s theorem for fractional variational problems of variable order

Noether’s theorem for non-smooth extremals of variational problems with time delay

Non-differentiable Solutions for Local Fractional Nonlinear Riccati Differential Equations ⬇️

Nondifferentiable variational principles in terms of a quantum operator

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Nonsymmetric and symmetric fractional calculi on arbitrary nonempty closed sets ⬇️

Numerical Solution of Variable-Order Fractional Differential Equations Using Bernoulli Polynomials

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Numerical analysis of a nonlocal parabolic problem resulting from thermistor problem

Numerical approximations of fractional derivatives with applications

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On a Fractional Oscillator Equation with Natural Boundary Conditions

On a Non-Newtonian Calculus of Variations

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On the Henstock-Kurzweil integral for Riesz-space-valued functions on time scales

On the two-dimensional rotational body of maximal Newtonian resistance

Optimal Control of a Dengue Epidemic Model with Vaccination

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Optimal Control with Time Delays via the Penalty Method ⬇️

Optimal Solutions to Relaxation in Multiple Control Problems of Sobolev Type with Nonlocal Nonlinear Fractional Differential Equations

Optimal control for a tuberculosis model with reinfection and post-exposure interventions.

scientific article published on 22 May 2013

Optimal control of a delayed HIV model

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Optimal control of a fractional order epidemic model with application to human respiratory syncytial virus infection

Optimal control of a tuberculosis model with state and control delays ⬇️

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Optimal control of non-autonomous SEIRS models with vaccination and treatment

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Optimal control of nonlocal thermistor equations

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Optimal control strategies for tuberculosis treatment: A case study in Angola

scholarly article published August 2012

Optimality conditions for fractional variational problems with dependence on a combined Caputo derivative of variable order ⬇️

Optimality conditions for the calculus of variations with higher-order delta derivatives

Optimization of Dengue Epidemics: A Test Case with Different Discretization Schemes

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Parameter Estimation, Sensitivity Analysis and Optimal Control of a Periodic Epidemic Model with Application to HRSV in Florida

Predicting and controlling the Ebola infection ⬇️

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Pressure responses of a vertically hydraulic fractured well in a reservoir with fractal structure ⬇️

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Proper extensions of Noether's symmetry theorem for nonsmooth extremals of the calculus of variations

Quantum Variational Calculus

Regularity of Solutions for the Autonomous Integrals of the Calculus of Variations

Regularity of solutions to higher-order integrals of the calculus of variations

Seasonality effects on dengue: basic reproduction number, sensitivity analysis and optimal control ⬇️

Sensitivity Analysis in a Dengue Epidemiological Model

scholarly article published 2013

Sobolev Type Fractional Dynamic Equations and Optimal Multi-Integral Controls with Fractional Nonlocal Conditions ⬇️

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Solutions of systems with the Caputo–Fabrizio fractional delta derivative on time scales

Solving Abel integral equations of first kind via fractional calculus ⬇️

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Some inequalities for interval-valued functions on time scales

Stability Analysis of Delayed COVID-19 Models

scientific article published in 2022

Stability and optimal control of a delayed HIV model ⬇️

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Study of a Fractional Creep Problem with Multiple Delays in Terms of Boltzmann’s Superposition Principle

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Symmetric differentiation on time scales

Symmetric duality for left and right Riemann–Liouville and Caputo fractional differences

Taylor’s Formula for Generalized Weighted Fractional Derivatives with Nonsingular Kernels

scientific article published in 2022

The Calculus of Variations

The Cape Verde International Days on Mathematics 2013

scholarly article published 2013

The Cape Verde International Days on Mathematics 2017

scholarly article by Delfim F. M. Torres et al published 27 February 2018 in Statistics, Optimization and Information Computing

The Diamond Integral on Time Scales

The DuBois–Reymond Fundamental Lemma of the Fractional Calculus of Variations and an Euler–Lagrange Equation Involving Only Derivatives of Caputo

The Duality Theory of Fractional Calculus and a New Fractional Calculus of Variations Involving Left Operators Only

scientific article published on 30 April 2024

The Fractional Calculus of Variations

The Fuzzy Henstock–Kurzweil Delta Integral on Time Scales

The Hahn Quantum Variational Calculus

scientific article published on 20 July 2010

The Legendre condition of the fractional calculus of variations

The Power Fractional Calculus: First Definitions and Properties with Applications to Power Fractional Differential Equations

scientific article published in 2022

The Second Euler-Lagrange Equation of Variational Calculus on Time Scales

article by Zbigniew Bartosiewicz et al published January 2011 in European Journal of Control

The contingent epiderivative and the calculus of variations on time scales

The effect of immigrant communities coming from higher incidence tuberculosis regions to a host country

The existence of solutions for dynamic inclusions on time scales via duality

Time scale differential, integral, and variational embeddings of Lagrangian systems

Towards a combined fractional mechanics and quantization

Transversality conditions for infinite horizon variational problems on time scales

Two-dimensional body of maximum mean resistance

Uniform asymptotic stability of a fractional tuberculosis model

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Vaccination models and optimal control strategies to dengue

scientific article published on January 2014

Variable order fractional variational calculus for double integrals

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Variational calculus with conformable fractional derivatives ⬇️

Variational problems of Herglotz type with time delay: DuBois--Reymond condition and Noether's first theorem ⬇️

Weighted Generalized Fractional Integration by Parts and the Euler–Lagrange Equation

scientific article published in 2022