An Efficient Analytical Technique for Time-Fractional Parabolic Partial Differential Equations

Muhammad Mustahsan,S Iqbal,Jagdev Singh,H M Younas,Sushila Rathore,Kottakkaran Sooppy Nisar

doi:10.3389/fphy.2020.00131

Abstract

In this work, we examine the time-fractional fourth-order parabolic partial differential equations with the aid of the optimal homotopy asymptotic method (OHAM). The 2nd order approximate results obtained by using the suggested scheme are compared with the exact solution. It has been noted that the results achieved via OHAM have a large convergence rate for the problems. The solutions are graphically analyzed, and the relative errors are presented in tabular form.

Highlights

The physical behaviors of fractional order differential and integral equations have been studied in fractional calculus (FC)
Based on the optimal homotopy asymptotic method (OHAM) scheme [18, 19], we will extend this approach for time-fractional parabolic partial differential equations (TFPPDE) in the subsequent steps
A detailed algorithm for OHAM is presented for parabolic equations of arbitrary fractional order, and a description is designed for the examples in the above section which gives remarkably valid results for the TFPPDEs without domain discretization

Summary

Introduction

The physical behaviors of fractional order differential and integral equations have been studied in fractional calculus (FC). Fractional calculus deals with more general behavior than classical calculus. Spanier and Oldham [1], Podlubny [2], and Miller and Rose [3], have studied this subject in detail and developed the theoretical explanation of the subject. During the last few decades, a large number of researchers have noted that the role of fractional differential or integral operators are unavoidable in representing the characteristics of physical phenomena like traffic flow, viscoelasticity, fluid flow, signal processing, etc., [4,5,6,7,8,9,10]. Comparative studies have been done for fractional and total differential models. The fractional models are more effective than classical models.

Methods

Discussion

Conclusion