相关论文: Computational Methods in the Fractional Calculus o…
We present a new numerical tool to solve partial differential equations involving Caputo derivatives of fractional variable order. Three Caputo-type fractional operators are considered, and for each one of them an approximation formula is…
We study operators that are generalizations of the classical Riemann-Liouville fractional integral, and of the Riemann-Liouville and Caputo fractional derivatives. A useful formula relating the generalized fractional derivatives is proved,…
In this study the general formula for differential and integral operations of fractional calculus via fractal operators by the method of cumulative diminution and cumulative growth is obtained. The under lying mechanism in the success of…
The aim of this paper is to exhibit a necessary and sufficient condition of optimality for functionals depending on fractional integrals and derivatives, on indefinite integrals and on presence of time delay. We exemplify with one example,…
We design and analyze solution techniques for a linear-quadratic optimal control problem involving the integral fractional Laplacian. We derive existence and uniqueness results, first order optimality conditions, and regularity estimates…
Recent studies have shown that fractional calculus is an effective alternative mathematical tool in various scientific fields. However, some investigations indicate that results established in differential and integral calculus do not…
We prove necessary optimality conditions, in the class of continuous functions, for variational problems defined with Jumarie's modified Riemann-Liouville derivative. The fractional basic problem of the calculus of variations with free…
We study fractional variational problems of Herglotz type of variable order. Necessary optimality conditions, described by fractional differential equations depending on a combined Caputo fractional derivative of variable order, are proved.…
We propose two efficient numerical approaches for solving variable-order fractional optimal control-affine problems. The variable-order fractional derivative is considered in the Caputo sense, which together with the Riemann-Liouville…
Considering the large number of fractional operators that exist, and since it does not seem that their number will stop increasing soon at the time of writing this paper, it is presented for the first time, as far as the authors know, a…
Distributed-order fractional non-local operators have been introduced and studied by Caputo at the end of the 20th century. They generalize fractional order derivatives/integrals in the sense that such operators are defined by a weighted…
This paper is concerned with analyzing a class of fractional calculus of variations problems and their associated Euler-Lagrange (fractional differential) equations. Unlike the existing fractional calculus of variations which is based on…
An analysis of a fractional cubic differential equation is presented, which is a generalization of different versions of fractional logistic equations, in order to obtain simpler numerical methods that globalize and extend the results…
This study reexamines diffusive representations for fractional integrals with the goal of pioneering new variants of such representations. These variants aim to offer highly efficient numerical algorithms for the approximate computation of…
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…
We survey the main numerical techniques for finite-dimensional nonlinear optimal control. The chapter is written as a guide to practitioners who wish to get rapidly acquainted with the main numerical methods used to efficiently solve an…
We use classical tools from calculus of variations to formally derive necessary conditions for a Markov control to be optimal in a standard finite time horizon stochastic control problem. As an example, we solve the well-known Merton…
This paper presents an efficient numerical technique for solving multi-dimensional fractional optimal control problems using fractional-order generalized Bernoulli wavelets. The numerical results obtained by this method have been compared…
In this PhD thesis we introduce a generalized fractional calculus of variations. We consider variational problems containing generalized fractional integrals and derivatives, and study them using standard (indirect) and direct methods. In…
In this paper we propose an algorithm for the numerical solution of arbitrary differential equations of fractional order. The algorithm is obtained by using the following decomposition of the differential equation into a system of…