相关论文: Comparative study of Three Numerical Schemes for F…

In this paper we construct a new difference analog of the Caputo fractional derivative (called the $L2$-$1_\sigma$ formula). The basic properties of this difference operator are investigated and on its basis some difference schemes…

A numerical scheme for solving fractional initial value problems involving the Atangana-Baleanu fractional derivative is presented. Some examples for the proposed method are included, both for equations and systems of fractional initial…

In this paper, we develop two fast implicit difference schemes for solving a class of variable-coefficient time-space fractional diffusion equations with integral fractional Laplacian (IFL). The proposed schemes utilize the graded $L1$…

The paper provides the fractional integrals and derivatives of the Rie\-mann-Liouville and Caputo type for the five kinds of radial basis functions (RBFs), including the powers, Gaussian, multiquadric, Matern and thin-plate splines, in one…

Finite difference schemes are here solved by means of a linear matrix equation. The theoretical study of the related algebraic system is exposed, and enables us to minimize the error due to a finite difference approximation.

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…

This paper detailedly discusses the locally one-dimensional numerical methods for efficiently solving the three-dimensional fractional partial differential equations, including fractional advection diffusion equation and Riesz fractional…

Numerical solving differential equations with fractional derivatives requires elimination of the singularity which is inherent in the standard definition of fractional derivatives. The method of integration by parts to eliminate this…

Conventional finite-difference schemes for solving partial differential equations are based on approximating derivatives by finite-differences. In this work, an alternative theory is proposed which view finite-difference schemes as…

The following document presents some novel numerical methods valid for one and several variables, which using the fractional derivative, allow to find solutions for some non-linear systems in the complex space using real initial conditions.…

This paper proposes specular differentiation in one-dimensional Euclidean space and provides its fundamental analysis, including a quasi-Fermat theorem and a quasi-Mean Value Theorem. As an application, this paper develops several numerical…

This chapter presents some numerical methods to solve problems in the fractional calculus of variations and fractional optimal control. Although there are plenty of methods available in the literature, we concentrate mainly on approximating…

We introduce a new numerical method, based on Bernoulli polynomials, for solving multiterm variable-order fractional differential equations. The variable-order fractional derivative was considered in the Caputo sense, while the…

In the paper we study the subject of positivity of systems with sequential fractional difference. We give formulas for the unique solutions of systems in linear and semi-linear cases. The positivity of systems is considered.

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…

We are concerned with the numerical resolution of backward stochastic differential equations. We propose a new numerical scheme based on iterative regressions on function bases, which coefficients are evaluated using Monte Carlo…

In this article, we explore the effectiveness of two polynomial methods in solving non-linear time and space fractional partial differential equations. We first outline the general methodology and then apply it to five distinct experiments.…

In this paper, we propose and analyze a spectral Chebyshev-Legendre approximation for fractional order integro-differential equations of Fredholm type. The fractional derivative is described in the Caputo sense. Our proposed method is…

In this paper we present a new type of fractional operator, the Caputo-Katugampola derivative. The Caputo and the Caputo-Hadamard fractional derivatives are special cases of this new operator. An existence and uniqueness theorem for a…

We propose an approximation of nonlinear renewal equations by means of ordinary differential equations. We consider the integrated state, which is absolutely continuous and satisfies a delay differential equation. By applying the…