We establish interior and up to the boundary Hölder regularity estimates for weak solutions of Dirichlet problem fractional g−Laplacian with bounded right hand side g convex. These are first results available in literature integro-differential equations context Orlicz–Sobolev spaces.

In this paper will be compared between Adomian decomposition method (ADM) and Taylor expansion method (TEM) for solving (approximately) a class of fractional integro-differential equations. Numerical examples are presented to illustrate the efficiency and accuracy of the proposed methods. General Terms Numerical solutions, Fractional integro-differential equations.

In this paper, a modification of variational iteration method is applied to solve fractional integro-differential equations. The fractional derivative is considered in the Caputo sense. Through examples, we will see the modified method performs extremely effective in terms of efficiency and simplicity to solve fractional integro-differential equations. 2000 Mathematics Subject Classification: 6...

The Laplace decomposition method (LDM) has been implemented on integro-differential equations to calculate the analytical exact solutions. Obtained results show the effectiveness, reliability and convergence of the proposed method. It may be concluded that the proposed method is a powerful tool for solving the integro-differential equations and other wide class of mathematical problems.

In this paper we study the existence of classical solutions for a class of abstract neutral integro-differential equation with unbounded delay. A concrete application to partial neutral integro-differential equations is considered.

Some new stability results are given for a delay integro-differential equation. A basis theorem on the behavior of solutions of delay integro-differential equations is established. As a consequence of this theorem, a stability criterion is obtained.

Most boundary element methods for two-dimensional boundary value problems are based on point collocation on the boundary and the use of splines as trial functions. Here we present a unified asymptotic error analysis for even as well as for odd degree splines subordinate to uniform or smoothly graded meshes and prove asymptotic convergence of optimal order. The equations are collocated at the br...

Abstract In this research study, we investigate the existence and uniqueness of solutions for a coupled multiorder system fractional differential equations involving integro-differential boundary conditions in Riemann–Liouville setting. The presented results are obtained via classical Banach principle along with Leray–Schauder Krasnosel’skiĭ’s fixed-point theorems. Examples included to support ...

A numerical scheme, based on the cubic B-spline wavelets for solving fractional integro-differential equations is presented. The fractional derivative of these wavelets are utilized to reduce the fractional integro-differential equation to system of algebraic equations. Numerical examples are provided to demonstrate the accuracy and efficiency and simplicity of the method.