Computational analysis of fractional modified Degasperis-Procesi equation with Caputo-Katugampola derivative

Jagdev Singh; Arpita Gupta; Jagdev Singh; Arpita Gupta

doi:10.3934/math.2023009

AIMS Mathematics

2023, Volume 8, Issue 1: 194-212. doi: 10.3934/math.2023009

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Computational analysis of fractional modified Degasperis-Procesi equation with Caputo-Katugampola derivative

Jagdev Singh ^,,
Arpita Gupta

Department of Mathematics, JECRC University, Jaipur, India

Received: 21 May 2022 Revised: 19 August 2022 Accepted: 19 August 2022 Published: 28 September 2022
MSC : 34A08, 35A20, 35A22, 35C05

Main aim of the current study is to examine the outcomes of nonlinear partial modified Degasperis-Procesi equation of arbitrary order by using two analytical methods. Both methods are based on homotopy and a novel adjustment with generalized Laplace transform operator. Nonlinear terms are handled by using He's polynomials. The fractional order modified Degasperis-Procesi (FMDP) equation, is capable to describe the nonlinear aspects of dispersive waves. The Katugampola derivative of fractional order in the caputo type is employed to model this problem. The numerical results and graphical representation demonstrate the efficiency and accuracy of applied techniques.
- Caputo-Katugampola fractional derivative,
- generalized Laplace transform,
- Degasperis-Procesi equation
Citation: Jagdev Singh, Arpita Gupta. Computational analysis of fractional modified Degasperis-Procesi equation with Caputo-Katugampola derivative[J]. AIMS Mathematics, 2023, 8(1): 194-212. doi: 10.3934/math.2023009

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Abstract

Main aim of the current study is to examine the outcomes of nonlinear partial modified Degasperis-Procesi equation of arbitrary order by using two analytical methods. Both methods are based on homotopy and a novel adjustment with generalized Laplace transform operator. Nonlinear terms are handled by using He's polynomials. The fractional order modified Degasperis-Procesi (FMDP) equation, is capable to describe the nonlinear aspects of dispersive waves. The Katugampola derivative of fractional order in the caputo type is employed to model this problem. The numerical results and graphical representation demonstrate the efficiency and accuracy of applied techniques.

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