Distributed-order fractional calculus (DOFC) is a rapidly emerging branch of the broader
area of fractional calculus that has important and far-reaching applications for the modeling …

Recently, operational matrices were adapted for solving several kinds of fractional
differential equations (FDEs). The use of numerical techniques in conjunction with …

This book provides efficient and reliable numerical methods for solving fractional calculus
problems. It focuses on numerical techniques for fractional integrals, derivatives, and …

In this paper, we derived the shifted Jacobi operational matrix (JOM) of fractional derivatives
which is applied together with spectral tau method for numerical solution of general linear …

In this paper, an efficient and accurate spectral numerical method is presented for solving
second-, fourth-order fractional diffusion-wave equations and fractional wave equations with …

In this paper, an analytical method based on the generalized Taylors series formula together
with residual error function, namely residual power series method (RPSM), is proposed for …

The current study aims to approximate the solution of fractional differential equations (FDEs)
by using the fundamental properties of artificial neural networks (ANNs) for function …

While several high-order methods have been developed for fractional PDEs (FPDEs) with
fixed order, there are no such methods for FPDEs with field-variable order. These equations …

This paper presents a direct solution technique for solving the generalized pantograph
equation with variable coefficients subject to initial conditions, using a collocation method …

In this article, we first propose a new numerical technique based upon a certain two-
dimensional extended differential transform via local fractional derivatives and derive its …