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Ata, Enes, Kıymaz, İ. Onur. (1403). New generalized special functions with two generalized M-series at their kernels and solution of fractional PDEs via double Laplace transform. سامانه مدیریت نشریات علمی, 12(1), 31-43. doi: 10.22034/cmde.2023.55800.2325
Enes Ata; İ. Onur Kıymaz. "New generalized special functions with two generalized M-series at their kernels and solution of fractional PDEs via double Laplace transform". سامانه مدیریت نشریات علمی, 12, 1, 1403, 31-43. doi: 10.22034/cmde.2023.55800.2325
Ata, Enes, Kıymaz, İ. Onur. (1403). 'New generalized special functions with two generalized M-series at their kernels and solution of fractional PDEs via double Laplace transform', سامانه مدیریت نشریات علمی, 12(1), pp. 31-43. doi: 10.22034/cmde.2023.55800.2325
Ata, Enes, Kıymaz, İ. Onur. New generalized special functions with two generalized M-series at their kernels and solution of fractional PDEs via double Laplace transform. سامانه مدیریت نشریات علمی, 1403; 12(1): 31-43. doi: 10.22034/cmde.2023.55800.2325

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

Computational Methods for Differential Equations
مقاله 3، دوره 12، شماره 1، فروردین 2024، صفحه 31-43    اصل مقاله (677.08 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2023.55800.2325
نویسندگان
Enes Ata* ؛ İ. Onur Kıymaz
Department of Mathematics, Kır¸sehir Ahi Evran University, Kır¸sehir, Turkey.
چکیده
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.
کلیدواژه‌ها
Double Laplace transform؛ Fractional partial differential equations؛ Beta function؛ Gauss hypergeometric function؛ Confluent hypergeometric function
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