Related papers: Substitution Method for Fractional Differential Eq…
The numerical methods for differential equation solution allow obtaining a discrete field that converges towards the solution if the method is applied to the correct problem. Nevertheless, the numerical methods have the restricted class of…
We present a new discretization for the Hadamard fractional derivative, that simplifies the computations. We then apply the method to solve a fractional differential equation and a fractional variational problem with dependence on the…
A generalization of exterior calculus is considered by allowing the partial derivatives in the exterior derivative to assume fractional orders. That is, a fractional exterior derivative is defined. This is found to generate new vector…
Solutions to fractional models inherently exhibit non-smooth behavior, which significantly deteriorates the accuracy and therefore efficiency of existing numerical methods. We develop a two-stage data-infused computational framework for…
The Adomian decomposition method is a semi-analytical method for solving ordinary and partial nonlinear differential equations. The aim of this paper is to apply Adomian decomposition method to obtain approximate solutions of nonlinear…
This paper deals with fractional differential equations, with dependence on a Caputo fractional derivative of real order. The goal is to show, based on concrete examples and experimental data from several experiments, that fractional…
Recently, a new fractional derivative called the conformable fractional derivative is given which is based on the basic limit definition of the derivative in [1]. Then, the fractional versions of chain rules, exponential functions,…
Fractional calculus is a powerful and effective tool for modelling nonlinear systems. The M derivative is the generalization of alternative fractional derivative. This M derivative obey the properties of integer calculus. In this paper, we…
The Cauchy problem for fractional derivatives linear systems of ordinary differential equations with constant coefficients is considered, where at first the analytic expressions are given through the matrix exponent of its corresponding…
In the paper titled "New numerical approach for fractional differential equations" by A. Atangana and K.M. Owolabi [Math. Model. Nat. Phenom., 13(1), 2018], it is presented a method for the numerical solution of some fractional differential…
In this paper, the solution of the multi-order differential equations, by using Mellin Transform, is proposed. It is shown that the problem related to the shift of the real part of the argument of the transformed function, arising when the…
The accuracy of the numerical solution of a fractional differential equation depends on the differentiability class of the solution. The derivatives of the solutions of fractional differential equations often have a singularity at the…
Using both fractional derivatives, defined in the Riemann-Liouville and Caputo senses, and classical derivatives of the integer order we examine different numerical approaches to ordinary differential equations. Generally we formulate some…
The method of characteristics has played a very important role in mathematical physics. Preciously, it was used to solve the initial value problem for partial differential equations of first order. In this paper, we propose a fractional…
This overview is devoted to splitting methods, a class of numerical integrators intended for differential equations that can be subdivided into different problems easier to solve than the original system. Closely connected with this class…
In this paper we discuss some issues that arise in the process of writing a fractional differential equation (FDE) by replacing an integer order derivative by a fractional order derivative in a given differential equation. To address these…
This article examines a new approach to solving ordinary differential equations based on Fractional-Calculus theory. Poisson and Sturm-Liouville-type problems are studied, together with different boundary conditions. Each case is analyzed…
Two approximations, derived from continuous expansions of Riemann-Liouville fractional derivatives into series involving integer order derivatives, are studied. Using those series, one can formally transform any problem that contains…
The solutions of fractional differential equations (FDEs) have a natural singularity at the initial point. The accuracy of their numerical solutions is lower than the accuracy of the numerical solutions of FDEs whose solutions are…
Fractional calculus generalizes the derivative and antiderivative operations of differential and integral calculus from integer orders to the entire complex plane. Methods are presented for using this generalized calculus with Laplace…