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

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.

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An Efficient Technique for Fractional Coupled System Arisen in Magnetothermoelasticity With Rotation Using Mittag–Leffler Kernel

Journal of Computational and Nonlinear Dynamics ◽

10.1115/1.4048577 ◽

2020 ◽

Vol 16 (1) ◽

Author(s):

P. Veeresha ◽

D. G. Prakasha ◽

Dumitru Baleanu

Keyword(s):

Fractional Order ◽

Nonlinear Differential Equations ◽

Coupled System ◽

Order Model ◽

Science And Engineering ◽

Transform Method ◽

Fractional Order Model ◽

Analysis Scheme ◽

Laplace Transform Technique ◽

Homotopy Analysis

Abstract In this paper, we find the solution for fractional coupled system arisen in magnetothermoelasticity with rotation using q-homotopy analysis transform method (q-HATM). The proposed technique is graceful amalgamations of Laplace transform technique with q-homotopy analysis scheme, and fractional derivative defined with Mittag–Leffler kernel. The fixed point hypothesis is considered to demonstrate the existence and uniqueness of the obtained solution for the proposed fractional order model. To illustrate the efficiency of the future technique, we analyzed the projected model in terms of fractional order. Moreover, the physical behavior of q-HATM solutions has been captured in terms of plots for different arbitrary order. The attained consequences confirm that the considered algorithm is highly methodical, accurate, very effective, and easy to implement while examining the nature of fractional nonlinear differential equations arisen in the connected areas of science and engineering.

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ITERATIVE METHOD APPLIED TO THE FRACTIONAL NONLINEAR SYSTEMS ARISING IN THERMOELASTICITY WITH MITTAG-LEFFLER KERNEL

Fractals ◽

10.1142/s0218348x2040040x ◽

2020 ◽

Vol 28 (08) ◽

pp. 2040040 ◽

Cited By ~ 9

Author(s):

WEI GAO ◽

P. VEERESHA ◽

D. G. PRAKASHA ◽

BILGIN SENEL ◽

HACI MEHMET BASKONUS

Keyword(s):

Fractional Order ◽

Nonlinear Differential Equations ◽

Order Model ◽

Science And Engineering ◽

One Dimensional ◽

Fractional Order Model ◽

Analysis Scheme ◽

Laplace Transform Technique ◽

Homotopy Analysis ◽

The One

In this paper, we study on the numerical solution of fractional nonlinear system of equations representing the one-dimensional Cauchy problem arising in thermoelasticity. The proposed technique is graceful amalgamations of Laplace transform technique with [Formula: see text]-homotopy analysis scheme and fractional derivative defined with Atangana–Baleanu (AB) operator. The fixed-point hypothesis is considered in order to demonstrate the existence and uniqueness of the obtained solution for the proposed fractional order model. In order to illustrate and validate the efficiency of the future technique, we consider three different cases and analyzed the projected model in terms of fractional order. Moreover, the physical behavior of the obtained solution has been captured in terms of plots for diverse fractional order, and the numerical simulation is demonstrated to ensure the exactness. The obtained results elucidate that the proposed scheme is easy to implement, highly methodical as well as accurate to analyze the behavior of coupled nonlinear differential equations of arbitrary order arisen in the connected areas of science and engineering.

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A novel approach for nonlinear equations occurs in ion acoustic waves in plasma with Mittag-Leffler law

Engineering Computations ◽

10.1108/ec-09-2019-0438 ◽

2020 ◽

Vol 37 (6) ◽

pp. 1865-1897 ◽

Cited By ~ 7

Author(s):

P. Veeresha ◽

D.G. Prakasha ◽

Jagdev Singh

Keyword(s):

Nonlinear Equations ◽

Fractional Order ◽

Nonlinear Differential Equations ◽

Content Type ◽

Physical Behaviour ◽

Special Cases ◽

Analysis Scheme ◽

Laplace Transform Technique ◽

The Future ◽

Homotopy Analysis

Purpose The purpose of this paper is to find the solution for special cases of regular-long wave equations with fractional order using q-homotopy analysis transform method (q-HATM). Design/methodology/approach The proposed technique (q-HATM) is the graceful amalgamations of Laplace transform technique with q-homotopy analysis scheme and fractional derivative defined with Atangana-Baleanu (AB) operator. Findings The fixed point hypothesis considered to demonstrate the existence and uniqueness of the obtained solution for the proposed fractional-order model. To illustrate and validate the efficiency of the future technique, the authors analysed the projected nonlinear equations in terms of fractional order. Moreover, the physical behaviour of the obtained solution has been captured in terms of plots for diverse fractional order. Originality/value To illustrate and validate the efficiency of the future technique, we analysed the projected nonlinear equations in terms of fractional order. Moreover, the physical behaviour of the obtained solution has been captured in terms of plots for diverse fractional order. The obtained results elucidate that, the proposed algorithm is easy to implement, highly methodical, as well as accurate and very effective to analyse the behaviour of nonlinear differential equations of fractional order arisen in the connected areas of science and engineering.

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New Numerical Results for the Time-Fractional Phi-Four Equation Using a Novel Analytical Approach

Symmetry ◽

10.3390/sym12030478 ◽

2020 ◽

Vol 12 (3) ◽

pp. 478 ◽

Cited By ~ 19

Author(s):

Wei Gao ◽

Pundikala Veeresha ◽

Doddabhadrappla Gowda Prakasha ◽

Haci Mehmet Baskonus ◽

Gulnur Yel

Keyword(s):

Fractional Order ◽

Particle Physics ◽

Order Model ◽

Wave Interactions ◽

Transform Method ◽

Fractional Order Model ◽

Special Cases ◽

Homotopy Analysis ◽

Nuclear Particle ◽

Klein Gordon

This manuscript investigates the fractional Phi-four equation by using q -homotopy analysis transform method ( q -HATM) numerically. The Phi-four equation is obtained from one of the special cases of the Klein-Gordon model. Moreover, it is used to model the kink and anti-kink solitary wave interactions arising in nuclear particle physics and biological structures for the last several decades. The proposed technique is composed of Laplace transform and q -homotopy analysis techniques, and fractional derivative defined in the sense of Caputo. For the governing fractional-order model, the Banach’s fixed point hypothesis is studied to establish the existence and uniqueness of the achieved solution. To illustrate and validate the effectiveness of the projected algorithm, we analyze the considered model in terms of arbitrary order with two distinct cases and also introduce corresponding numerical simulation. Moreover, the physical behaviors of the obtained solutions with respect to fractional-order are presented via various simulations.

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The multi-step homotopy analysis method for solving fractional-order model for HIV infection of CD4+T cells

Proyecciones (Antofagasta) ◽

10.4067/s0716-09172015000400001 ◽

2015 ◽

Vol 34 (4) ◽

pp. 307-322 ◽

Cited By ~ 1

Author(s):

AH H. Handam ◽

Asad A. Freihat ◽

M. Zurigat

Keyword(s):

T Cells ◽

Hiv Infection ◽

Fractional Order ◽

Homotopy Analysis Method ◽

Cd4 T Cells ◽

Analysis Method ◽

Order Model ◽

Fractional Order Model ◽

Homotopy Analysis

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An efficient hybrid technique for the solution of fractional-order partial differential equations

Carpathian Mathematical Publications ◽

10.15330/cmp.13.3.790-804 ◽

2021 ◽

Vol 13 (3) ◽

pp. 790-804

Author(s):

H.K. Jassim ◽

H. Ahmad ◽

A. Shamaoon ◽

C. Cesarano

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Fractional Order ◽

Hybrid Technique ◽

Science And Engineering ◽

Partial Differential ◽

Transform Method ◽

Suggested Technique ◽

Homotopy Analysis ◽

Sumudu Transform

In this paper, a hybrid technique called the homotopy analysis Sumudu transform method has been implemented solve fractional-order partial differential equations. This technique is the amalgamation of Sumudu transform method and the homotopy analysis method. Three examples are considered to validate and demonstrate the efficacy and accuracy of the present technique. It is also demonstrated that the results obtained from the suggested technique are in excellent agreement with the exact solution which shows that the proposed method is efficient, reliable and easy to implement for various related problems of science and engineering.

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