A novel hybrid technique to obtain the solution of generalized fractional-order differential equations

The motive of the work is to propose a new hybrid technique, the Homotopy Perturbation General Transform Method (HPGTM) for obtaining an analytic solution for a wide class of time-fractional differential equations in the Caputo sense. The efficiency of HPGTM is analyzed using a comparative study wit...

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Bibliographic Details
Published inMathematics and computers in simulation Vol. 205; pp. 272 - 290
Main Authors Khirsariya, Sagar R., Rao, Snehal B., Chauhan, Jignesh P.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.03.2023
Subjects
Caputo fractional derivative
Fractional differential equation
General transform
Homotopy perturbation method
Fractional differential equation
Homotopy perturbation method
General transform
Caputo fractional derivative
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ISSN0378-4754
1872-7166
DOI10.1016/j.matcom.2022.10.013

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Summary:The motive of the work is to propose a new hybrid technique, the Homotopy Perturbation General Transform Method (HPGTM) for obtaining an analytic solution for a wide class of time-fractional differential equations in the Caputo sense. The efficiency of HPGTM is analyzed using a comparative study with Adomian Decomposition Method (ADM), Residual Power Series Method (RPSM), and exact solution. Numerical examples including well-known equations viz. radioactive decay model, Riccati equation, backward Kolmogorov equation, Klein–Gordon equation, and Rosenau–Hyman equation are considered in arbitrary order. The outcomes of numerical simulations clearly state the effectiveness of the present method.
ISSN:0378-4754
1872-7166
DOI:10.1016/j.matcom.2022.10.013