In this paper, a new operational matrix method based on Haar wavelets is proposed to solve
linear and non-linear differential equations of fractional order. Contrary to wavelet …

In this paper, the linear B-spline scaling functions and wavelets operational matrix of
fractional integration are derived. A new approach implementing the linear B-spline scaling …

In this study, we present two highly effective approaches aimed at solving linear systems of
equations, specifically focusing on the Fredholm and Volterra equations in fractional integro …

In this paper, generalized fractional-order Legendre functions (GFLFs) are used to introduce
a new operational-projection method for numerical solution of a class of partial differential …

This paper describes and compares application of wavelet basis and Block-Pulse functions
(BPFs) for solving fractional integro-differential equation (FIDE) with a weakly singular …

A new technique for solving a system of fractional Fredholm integro-differential equations
(IDEs) is introduced in this manuscript. Furthermore, we present a review for the derivation of …

Mathematical models and computer simulations are useful experimental tools for building
and testing theories. Many mathematical models in biology can be formulated by a nonlinear …

Nowadays, the operational matrix plays an important role insolving problems with partial,
ordinary or fractional derivatives. In thecurrent study, we construct the operational matrix of …

In this paper, functional Hammerstein integro-differential equations of fractional order is
studied. Here the existence and uniqueness of the solution is proved. A numerical method to …

We construct two-dimensional hybrid functions from Lagrange polynomials and block-pulse-
functions. Using special properties of the functions for evaluating integral and derivatives …