A reliable analytical technique for fractional Caudrey-Dodd-Gibbon equation with Mittag-Leffler kernel

P Veeresha,D G Prakasha

doi:10.1515/nleng-2020-0018

Abstract

AbstractThe pivotal aim of the present work is to find the solution for fractional Caudrey-Dodd-Gibbon (CDG) equation using q-homotopy analysis transform method (q-HATM). The considered technique is graceful amalgamations of Laplace transform technique with q-homotopy analysis scheme, and fractional derivative defined with Atangana-Baleanu (AB) operator. The fixed point hypothesis considered in order to demonstrate the existence and uniqueness of the obtained solution for the projected fractional-order model. In order to illustrate and validate the efficiency of the future technique, we analysed the projected model in terms of fractional order. Moreover, the physical behaviour of q-HATM solutions have been captured in terms of plots for diverse fractional order and the numerical simulation is also demonstrated. The obtained results elucidate that, the considered algorithm is easy to implement, highly methodical as well as accurate and very effective to examine the nature of nonlinear differential equations of arbitrary order arisen in the connected areas of science and engineering.

Highlights

Fractional calculus (FC) was originated in Newton’s time, but lately, it fascinated the attention of many scholars
The pivotal aim of the present work is to nd the solution for fractional Caudrey-Dodd-Gibbon (CDG) equation using q-homotopy analysis transform method (q-HATM)
Since fractional Caudrey-Dodd-Gibbon (FCDG) equation plays a signi cant role in portraying several nonlinear phenomena and which are the generalizations of diverse complex phenomena, many authors nd and analysed the solution using analytical as well as numerical schemes [54,55,56,57,58,59,60,61]

Summary

Introduction

Fractional calculus (FC) was originated in Newton’s time, but lately, it fascinated the attention of many scholars. From the last thirty years, the most intriguing leaps in. The above equation is a class of KdV equation and further, it possesses distinct and diverse properties. The CGD equation is familiar as Sawada-Kotera equation [37]. Due to the importance of the considered problem, it has been magnetized the attention of many researchers from diverse areas. In 1984, Weiss illustrated the Painleve’ property for the Eq (1) [38]. Many important and nonlinear models are methodically and e ectively analysed with the help of fractional calculus. There have been diverse de nitions are suggested by many senior research scholars, for instance, Riemann, Liouville, Caputo and Fabrizio

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ABC a

AB a

Solution for FCDG equation

Conclusion