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In this article, we deal with the efficient computation of the Wright function in the cases of interest for the expression of solutions of some fractional differential equations. The proposed algorithm is based on the inversion of the…

Numerical Analysis · Mathematics 2024-09-16 Lidia Aceto , Fabio Durastante

Optimal control theory aims to find an optimal protocol to steer a system between assigned boundary conditions while minimizing a given cost functional in finite time. Equations arising from these types of problems are often non-linear and…

Optimization and Control · Mathematics 2025-02-21 Julia Sanders , Paolo Muratore-Ginanneschi

We describe a general operational method that can be used in the analysis of fractional initial and boundary value problems with additional analytic conditions. As an example, we derive analytic solutions of some fractional generalisation…

Analysis of PDEs · Mathematics 2013-04-04 Roberto Garra , Federico Polito

This article describes an approximation technique based on fractional order Bernstein wavelets for the numerical simulations of fractional oscillation equations under variable order, and the fractional order Bernstein wavelets are derived…

Numerical Analysis · Mathematics 2023-06-05 Ashish Rayal , Bhagawati Prasad Joshi , Mukesh Pandey , Delfim F. M. Torres

In this research, a new numerical method is proposed for solving fractional Bratu type boundary value problems. Fractional derivatives are taken in Caputo sense. This method is predicated on iterative approach of reproducing kernel Hilbert…

Numerical Analysis · Mathematics 2018-05-31 Mehmet Giyas Sakar , Onur Saldır , Ali Akgül

In this work, a new collocation approach using a combination of a wavelet operational matrix method and the exponential spline interpolation is proposed to solve the time-fractional convection-diffusion equation with variable coefficients.…

Numerical Analysis · Mathematics 2016-09-27 Xiaogang Zhu , Yufeng Nie

The paper is devoted to the development of control procedures with a guide for conflict-controlled dynamical systems described by ordinary fractional differential equations with the Caputo derivative of an order $\alpha \in (0, 1).$ For the…

Optimization and Control · Mathematics 2019-01-10 Mikhail Gomoyunov

Two key challenges in optimal control include efficiently solving high-dimensional problems and handling optimal control problems with state-dependent running costs. In this paper, we consider a class of optimal control problems whose…

Optimization and Control · Mathematics 2023-05-16 Paula Chen , Jérôme Darbon , Tingwei Meng

The application of the approximation-operational approach to solving linear differential equations of fractional order with variable coefficients is considered. It is shown that the method can also be applied to solving differential…

Dynamical Systems · Mathematics 2020-06-04 Oleksii V. Vasyliev

We propose a direct numerical method for the solution of an optimal control problem governed by a two-side space-fractional diffusion equation. The presented method contains two main steps. In the first step, the space variable is…

Optimization and Control · Mathematics 2019-01-29 Mushtaq Salh Ali , Mostafa Shamsi , Hassan Khosravian-Arab , Delfim F. M. Torres , Farid Bozorgnia

A geometric derivation of numerical integrators for optimal control problems is proposed. It is based in the classical technique of generating functions adapted to the special features of optimal control problems.

Optimization and Control · Mathematics 2025-10-20 M. de Leon , D. Martin de Diego , A. Santamaria-Merino

In this article, we study a fractional control problem that models the maximization of the profits obtained by exploiting a certain resource whose dynamics are governed by the fractional logistic equation. Due to the singularity of this…

Optimization and Control · Mathematics 2021-04-12 Melani Barrios , Gabriela Reyero , Mabel Tidball

This paper introduces a new accurate model for periodic fractional optimal control problems (PFOCPs) using Riemann-Liouville (RL) and Caputo fractional derivatives (FDs) with sliding fixed memory lengths. The paper also provides a novel…

Optimization and Control · Mathematics 2023-09-26 Kareem T. Elgindy

This paper presents a modified numerical scheme for a class of Fractional Optimal Control Problems (FOCPs) formulated in Agrawal (2004) where a Fractional Derivative (FD) is defined in the Riemann-Liouville sense. In this scheme, the entire…

Mathematical Physics · Physics 2008-11-27 Dumitru Baleanu , Ozlem Defterli , Om P. Agrawal

A matrix method for the solution of direct fractional Sturm-Liouville problems on bounded domain is proposed where the fractional derivative is defined in the Riesz sense. The scheme is based on the application of the Galerkin spectral…

Numerical Analysis · Mathematics 2017-04-06 Paolo Ghelardoni , Cecilia Magherini

We consider a Bolza-type optimal control problem for a dynamical system described by a fractional differential equation with the Caputo derivative of an order $\alpha \in (0, 1)$. The value of this problem is introduced as a functional in a…

Optimization and Control · Mathematics 2019-08-06 Mikhail I. Gomoyunov

In this paper we present a numerical solution of a two-phase fractional Stefan problem with time derivative described in the Caputo sense. In the proposed algorithm, we use a special case of front-fixing method supplemented by the iterative…

Numerical Analysis · Mathematics 2018-10-30 Marek Błasik

This article provides an effective computational algorithm based on Legendre wavelet (LW) and standard tau approach to approximate the solution of multi-dimensional distributed order time-space fractional weakly singular integro-partial…

Numerical Analysis · Mathematics 2022-06-01 Yashveer Kuma , Somveer Singh , Reshma Singh , Vineet Kumar Singh

In this paper, we study a class of fractional optimal control problems. A necessary condition for the existence of an optimal control is provided in the literature. It is commonly given as the existence of a solution of a fractional…

Optimization and Control · Mathematics 2012-03-08 Loïc Bourdin

We consider a bilinear optimal control for an evolution equation involving the fractional Laplace operator of order $0<s<1$. We first give some existence and uniqueness results for the considered evolution equation. Next, we establish some…

Optimization and Control · Mathematics 2024-11-26 Gisèle Mophou , Cyrille Kenne , Mahamadi Warma