New generalized special functions with two generalized M-series at their kernels and solution of fractional PDEs via double Laplace transform

Document Type : Research Paper

Authors

Department of Mathematics, Kır¸sehir Ahi Evran University, Kır¸sehir, Turkey.

Abstract

In this paper, we introduce three types of generalized special functions: beta, Gauss hypergeometric, and confluent hypergeometric, all involving two generalized M-series at their kernels. We then give several properties of these functions, such as integral representations, functional relations, summation relations, derivative formulas, transformation formulas, and double Laplace transforms. Furthermore, we obtain solutions of fractional partial differential equations involving these new generalized special functions and then we present graphs of the approximate behavior of the solutions. Also, we introduce a new generalized beta distribution and incomplete beta function. Finally, we establish relationships between the new generalized special functions and other generalized special functions found in the literature.

Keywords

References

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Computational Methods for Differential Equations
Volume 12, Issue 1
January 2024
Pages 31-43

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History

  • Receive Date: 11 March 2023
  • Revise Date: 02 August 2023
  • Accept Date: 19 August 2023

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