Analytical Solution of Generalized Bratu-Type Fractional Differential Equations Using the Homotopy Perturbation Transform Method

In this study, we present the generalized form of the higher-order nonlinear fractional Bratu-type equation. In this generalization, we deal with a generalized fractional derivative, which is quite useful from an application point of view. Furthermore, some special cases of the generalized fractiona...

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Bibliographic Details
Published inAxioms Vol. 13; no. 2; p. 133
Main Authors Alhamzi, Ghaliah, Gouri, Aafrin, Alkahtani, Badr Saad T., Dubey, Ravi Shanker
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.02.2024
Subjects
Applied mathematics
Calculus
Decomposition
Differential equations
Exact solutions
fractional Bratu-type equation
Fractional calculus
generalized fractional derivative
homotopy perturbation transform method
Homotopy theory
Integrals
Mathematical analysis
Mathematicians
Nonlinear differential equations
Perturbation
Perturbation (Mathematics)
Science
Tests, problems and exercises
Transformations (Mathematics)
India
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Summary:In this study, we present the generalized form of the higher-order nonlinear fractional Bratu-type equation. In this generalization, we deal with a generalized fractional derivative, which is quite useful from an application point of view. Furthermore, some special cases of the generalized fractional Bratu equation are recognized and examined. To solve these nonlinear differential equations of fractional order, we employ the homotopy perturbation transform method. This work presents a useful computational method for solving these equations and advances our understanding of them. We also plot some numerical outcomes to show the efficiency of the obtained results.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms13020133