LOCAL FRACTIONAL VARIATIONAL ITERATION METHOD FOR SOLVING VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS WITHIN LOCAL FRACTIONAL OPERATORS

Ammar Ali Neamah

doi:10.3844/jmssp.2014.401.407

Abstract

The paper uses the Local fractional variational Iteration Method for solving the second kind Volterra integro-differential equations within the local fractional integral operators. The analytical solutions within the non-differential terms are discussed. Some illustrative examples will be discussed. The obtained results show the simplicity and efficiency of the present technique with application to the problems for the integral equations.

Highlights

INTRODUCTIONThe theory of local fractional calculus is one of useful tools to process the fractal and continuously non differentiable functions (Kolwankar and Gangal, 1998; He, 2011; He et al, 2012; Parvate and Gangal, 2009; Carpinteri et al, 2004; Yang, 2011a; 2011b; 2011c)
The theory of local fractional calculus is one of useful tools to process the fractal and continuously non differentiable functions (Kolwankar and Gangal, 1998; He, 2011; He et al, 2012; Parvate and Gangal, 2009; Carpinteri et al, 2004; Yang, 2011a; 2011b; 2011c). It was successfully applied in local fractional FokkerPlanck equation (Kolwankar and Gangal, 1998), the fractal heat conduction equation (He, 2011; Yang, 2011c), fractal-time dynamical systems (Parvate and Gangal, 2009), fractal elasticity (Carpinteri et al, 2004), local fractional diffusion equation (Yang, 2011c), local fractional Laplace equation (Yang, 2011b; 2012a), local fractional integral equations (Yang, 2012b; 2012c; 2012d), local fractional differential equations (Yang, 2012e; Zhong et al, 2012; Zhong and Gao, 2011), fractal wave equation (Yang, 2011b; 2012a; Yang and Baleanu, 2012)
The method, which accurately computes the solutions in a local fractional series form or in an exact form, presents interest to applied sciences for problems where the other methods cannot be applied properly

Summary

INTRODUCTION

The theory of local fractional calculus is one of useful tools to process the fractal and continuously non differentiable functions (Kolwankar and Gangal, 1998; He, 2011; He et al, 2012; Parvate and Gangal, 2009; Carpinteri et al, 2004; Yang, 2011a; 2011b; 2011c).

PRELIMINARY DEFINITIONS

ANALYSIS OF THE METHOD

ILLUSTRATIVE EXAMPLES

CONCLUSION