Numerical Solution for Complex Systems of Fractional Order

Rabha W Ibrahim

doi:10.1155/2012/678174

Abstract

By using a complex transform, we impose a system of fractional order in the sense of Riemann-Liouville fractional operators. The analytic solution for this system is discussed. Here, we introduce a method of homotopy perturbation to obtain the approximate solutions. Moreover, applications are illustrated.

Highlights

Fractional models have been studied by many researchers to sufficiently describe the operation of variety of computational, physical, and biological processes and systems
Considerable attention has been paid to the solution of fractional differential equations, integral equations, and fractional partial differential equations of physical phenomena
We suggested two types of complex transforms for systems of fractional differential equations

Summary

Introduction

Fractional models have been studied by many researchers to sufficiently describe the operation of variety of computational, physical, and biological processes and systems. Considerable attention has been paid to the solution of fractional differential equations, integral equations, and fractional partial differential equations of physical phenomena Most of these fractional differential equations have analytic solutions, approximation, and numerical techniques 1–3. One of the most frequently used tools in the theory of fractional calculus is furnished by the Riemann-Liouville operators. It possesses advantages of fast convergence, higher stability, and higher accuracy to derive different types of numerical algorithms. The time is taken in sense of the Riemann-Liouville fractional operators. This type of differential equation arises in many interesting applications. Applications are imposed such as wave equations of fractional order

Fractional Calculus

Complex Transforms

Numerical Solution

Applications

Conclusion