LADM procedure to find the analytical solutions of the nonlinear fractional dynamics of partial integro-differential equations

Qasim KHAN, Hassan KHAN, Poom KUMAM, Fairouz TCHIER, Gurpreet SINGH

Research output: Contribution to journalArticlespeer-review

Abstract

Generally, fractional partial integro-differential equations (FPIDEs) play a vital role in modeling various complex phenomena. Because of the several applications of FPIDEs in applied sciences, mathematicians have taken a keen interest in developing and utilizing the various techniques for its solutions. In this context, the exact and analytical solutions are not very easy to investigate the solution of FPIDEs. In this article, a novel analytical approach that is known as the Laplace adomian decomposition method is implemented to calculate the solutions of FPIDEs. We obtain the approximate solution of the nonlinear FPIDEs. The results are discussed using graphs and tables. The graphs and tables have shown the greater accuracy of the suggested method compared to the extended cubic-B splice method. The accuracy of the suggested method is higher at all fractional orders of the derivatives. A sufficient degree of accuracy is achieved with fewer calculations with a simple procedure. The presented method requires no parametrization or discretization and, therefore, can be extended for the solutions of other nonlinear FPIDEs and their systems. Copyright © 2024 the author(s), published by De Gruyter.

Original languageEnglish
Article number20230101
JournalDemonstratio Mathematica
Volume57
Issue number1
Early online dateFeb 2024
DOIs
Publication statusPublished - 2024

Citation

Khan, Q., Khan, H., Kuman, P., Tchier, F., & Singh, D. (2024). LADM procedure to find the analytical solutions of the nonlinear fractional dynamics of partial integro-differential equations. Demonstratio Mathematica, 57(1), Article 20230101. https://doi.org/10.1515/dema-2023-0101

Keywords

  • Approximate solution
  • Laplace transformation
  • Adomian decomposition method
  • Caputo derivative operator
  • Analytical method
  • PG student publication

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