Analytical treatment of Volterra integro-differential equations of fractional order

Analytical Treatment of Volterra Integro-Differential Equations of Fractional Derivatives

In this paper the solution of the Volterra integro-differential equations of fractional order is presented. The proposed method consists in constructing the functional series, sum of which determines the function giving the solution of considered problem. We derive conditions under which the solution series, constructed by the method is convergent. Some examples are presented to verify convergen...

Yang-Laplace transform method Volterra and Abel's integro-differential equations of fractional order

This study outlines the local fractional integro-differential equations carried out by the local fractional calculus. The analytical solutions within local fractional Volterra and Abel’s integral equations via the Yang-Laplace transform are discussed. Some illustrative examples will be discussed. The obtained results show the simplicity and efficiency of the present technique with application t...

The analytical solutions for Volterra integro-differential equations within Local fractional operators by Yang-Laplace transform

In this paper, we apply the local fractional Laplace transform method (or Yang-Laplace transform) on Volterra integro-differential equations of the second kind within the local fractional integral operators to obtain the analytical approximate solutions. The iteration procedure is based on local fractional derivative operators. This approach provides us with a convenient way to find a solution ...

Analytical-Approximate Solution for Nonlinear Volterra Integro-Differential Equations

In this work, we conduct a comparative study among the combine Laplace transform and modied Adomian decomposition method (LMADM) and two traditional methods for an analytic and approximate treatment of special type of nonlinear Volterra integro-differential equations of the second kind. The nonlinear part of integro-differential is approximated by Adomian polynomials, and the equation is reduce...

Numerical Solution of Volterra Integro-differential Equations of Fractional Order by Laplace Decomposition Method