Integral equations are one of the most useful mathematical tools in both pure and applied analysis. This is particularly true of problems in mechanical vibrations and the related fields of engineering and mathematical physics. We can find numerous applications of differential and integral equations of fractional order in viscoelasticity, electrochemistry, control, porous media, electromagnetism...

We derive estimates for the solutions to differential equations driven by a Hölder continuous function of order β > 1/2. As an application we deduce the existence of moments for the solutions to stochastic partial differential equations driven by a fractional Brownian motion with Hurst parameter H > 1 2 .

in this paper, we investigate some problems which can be reduced to the goursat problem for afourth order equation. some results and theorems are given concerning the existence and uniqence for thesolution of the suggested problem.

We derive estimates for the solutions to differential equations driven by a Hölder continuous function of order β > 1/2. As an application we deduce the existence of moments for the solutions to stochastic partial differential equations driven by a fractional Brownian motion with Hurst parameter H > 1 2 .

In this article we review the Adomian decomposition method (ADM) and its modifications including different modified and parametrized recursion schemes, the multistage ADM for initial value problems as well as the multistage ADM for boundary value problems, new developments of the method and its applications to linear or nonlinear and ordinary or partial differential equations, including fractio...

Fractional inequalities are useful in establishing the uniqueness of solution for partial differential equations of fractional order. Also they provide upper and lower bounds for solutions of fractional boundary value problems. In this paper we obtain some general integral inequalities containing generalized Mittag-Leffler function and some already known integral inequalities have been produced...

this paper presents a new numerical method for solution of eikonal equation in two dimensions.in contrast to the previously developed methods which try to define the solution surface by its level sets(contour curves), the developed methodology identifies the solution surface by resorting to its characteristics. the suggested procedure is based on the geometric properties of the solution surface...