A Numerical Investigation of Systems of Partial Differential Equations Under Non-Singular Kernel

Nisha Meena; Shilpy Jain; Yogesh Khandelwal; Murli Manohar Gour; Praveen Agarwal

doi:10.18576/pfda/110401

A Numerical Investigation of Systems of Partial Differential Equations Under Non-Singular Kernel

Nisha Meena
, Shilpy Jain
, Yogesh Khandelwal
, Murli Manohar Gour
, Praveen Agarwal

Jaipur National University
Poornima College of Engineering
Vivekananda Global University
Saveetha Institute of Medical and Technical Sciences (Deemed to be University)
International College of Engineering

Research output: Contribution to journal › Article › peer-review

Abstract

This article investigates systems of nonlinear fractional partial differential equations (NFPDEs) utilizing the Shehu Adomian decomposition method (STDM) with a non-singular kernel. The STDM is combining the Shehu transform method with the Adomian decomposition method, providing exact and analytical solutions of systems of nonlinear fractional partial differential equations. The convergence and existence results for the suggested technique are presented. Two numerical examples are used to demonstrate the reliability and efficacy of proposed technique using Matlab software. The findings demonstrate that accurate and reliable approximations can be achieved in only a few terms.

Original language	English
Pages (from-to)	641-652
Number of pages	12
Journal	Progress in Fractional Differentiation and Applications
Volume	11
Issue number	4
DOIs	https://doi.org/10.18576/pfda/110401
State	Published - Oct 2025
Externally published	Yes

Keywords

Adomian polynomial
Caputo-Fabrizio derivative
Fractional partial differential equations
Shehu transform
existence
fixed point theory

Access to Document

10.18576/pfda/110401

Cite this

@article{16da4384d2ba48f3813af3c1466b04d0,

title = "A Numerical Investigation of Systems of Partial Differential Equations Under Non-Singular Kernel",

abstract = "This article investigates systems of nonlinear fractional partial differential equations (NFPDEs) utilizing the Shehu Adomian decomposition method (STDM) with a non-singular kernel. The STDM is combining the Shehu transform method with the Adomian decomposition method, providing exact and analytical solutions of systems of nonlinear fractional partial differential equations. The convergence and existence results for the suggested technique are presented. Two numerical examples are used to demonstrate the reliability and efficacy of proposed technique using Matlab software. The findings demonstrate that accurate and reliable approximations can be achieved in only a few terms.",

keywords = "Adomian polynomial, Caputo-Fabrizio derivative, Fractional partial differential equations, Shehu transform, existence, fixed point theory",

author = "Nisha Meena and Shilpy Jain and Yogesh Khandelwal and Gour, \{Murli Manohar\} and Praveen Agarwal",

note = "Publisher Copyright: {\textcopyright} 2025 NSP.",

year = "2025",

month = oct,

doi = "10.18576/pfda/110401",

language = "English",

volume = "11",

pages = "641--652",

journal = "Progress in Fractional Differentiation and Applications",

issn = "2356-9336",

publisher = "Natural Sciences Publishing",

number = "4",

}

TY - JOUR

T1 - A Numerical Investigation of Systems of Partial Differential Equations Under Non-Singular Kernel

AU - Meena, Nisha

AU - Jain, Shilpy

AU - Khandelwal, Yogesh

AU - Gour, Murli Manohar

AU - Agarwal, Praveen

PY - 2025/10

Y1 - 2025/10

N2 - This article investigates systems of nonlinear fractional partial differential equations (NFPDEs) utilizing the Shehu Adomian decomposition method (STDM) with a non-singular kernel. The STDM is combining the Shehu transform method with the Adomian decomposition method, providing exact and analytical solutions of systems of nonlinear fractional partial differential equations. The convergence and existence results for the suggested technique are presented. Two numerical examples are used to demonstrate the reliability and efficacy of proposed technique using Matlab software. The findings demonstrate that accurate and reliable approximations can be achieved in only a few terms.

AB - This article investigates systems of nonlinear fractional partial differential equations (NFPDEs) utilizing the Shehu Adomian decomposition method (STDM) with a non-singular kernel. The STDM is combining the Shehu transform method with the Adomian decomposition method, providing exact and analytical solutions of systems of nonlinear fractional partial differential equations. The convergence and existence results for the suggested technique are presented. Two numerical examples are used to demonstrate the reliability and efficacy of proposed technique using Matlab software. The findings demonstrate that accurate and reliable approximations can be achieved in only a few terms.

KW - Adomian polynomial

KW - Caputo-Fabrizio derivative

KW - Fractional partial differential equations

KW - Shehu transform

KW - existence

KW - fixed point theory

UR - https://www.scopus.com/pages/publications/105017584163

U2 - 10.18576/pfda/110401

DO - 10.18576/pfda/110401

M3 - Article

AN - SCOPUS:105017584163

SN - 2356-9336

VL - 11

SP - 641

EP - 652

JO - Progress in Fractional Differentiation and Applications

JF - Progress in Fractional Differentiation and Applications

IS - 4

ER -

A Numerical Investigation of Systems of Partial Differential Equations Under Non-Singular Kernel

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this