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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
مراجع
  • [1] U. M. Abubakar, A study of extended beta and associated functions connected to Fox-Wright function, J. Frac. Calculus Appl., 12(3) (2021), 1–23.
  • [2] G. E. Andrews, R. Askey, and R. Roy, Special functions, Cambridge University Press, Cambridge, 1999.
  • [3] A. M. O. Anwar, F. Jarad, D. Baleanu, and F. Ayaz, Fractional Caputo heat equation within the double Laplace transform, Rom. Journ. Phys., 58(1-2) (2013), 15–22.
  • [4] V. Ya. Arsenin, Basic equations and special functions of mathematical physics, Iliffe Books Ltd, London, 1968.
  • [5] E. Ata and I˙. O. Kıymaz, A study on certain properties of generalized special functions defined  by  Fox-Wright function, Appl. Math. Nonlinear Sci., 5(1) (2020), 147–162.
  • [6] E. Ata, Generalized beta function defined by Wright function, arXiv:1803.03121v3 [math.CA], (2021).
  • [7] E. Ata, Modified special functions defined by generalized M-series and their properties, arXiv:2201.00867v1 [math.CA], (2022).
  • [8] E. Ata, and I˙. O. Kıymaz, Generalized gamma, beta and hypergeometric functions defined by Wright function and applications to fractional differential equations, Cumhuriyet Sci. J., 43(4) (2022), 684–695.
  • [9] W. W. Bell, Special functions for scientists and engineers, Dover Publications, New York, 2013.
  • [10] M. A. Chaudhry, A. Qadir, M. Rafique, and S. M. Zubair, Extension of Euler’s beta function, J. Comput. Appl. Math., 78 (1997), 19–32.
  • [11] M. A. Chaudhry, A. Qadir, H. M. Srivastava, and R. B. Paris, Extended hypergeometric and confluent hypergeo- metric functions, Appl. Math. Comput., 159 (2004), 589–602.
  • [12] J. Choi, A. K. Rathie, and R. K. Parmar, Extension of extended beta, hypergeometric and confluent hypergeometric functions, Honam Math. J., 36 (2014), 357–385.
  • [13] A. C¸ etinkaya, I˙. O. Kıymaz, P. Agarwal, and R. A. Agarwal, A comparative study on generating function relations for generalized hypergeometric functions via generalized fractional operators, Adv. Differ. Equ., 2018(1) (2018), 1–11.
  • [14] L. Debnath, The double Laplace transforms and their properties with applications to functional, integral  and  partial differential equations, Int. J. Appl. Comput. Math., 2 (2016), 223–241.
  • [15] A. Goswami, S. Jain, P. Agarwal, and S. Aracı, A note on the new extended beta and Gauss hypergeometric functions, Appl. Math. Infor. Sci., 12 (2018), 139–144.
  • [16] A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and applications of fractional differential, North-Holland Mathematics Studies 204, 2006.
  • [17] D. M. Lee, A. K. Rathie, R. K. Parmar, and Y. S. Kim, Generalization  of  extended  beta  function,  hypergeometric  and confluent hypergeometric functions, Honam Math. J., 33 (2011), 187–206.
  • [18] F. Mainardi, Special functions with applications to mathematical physics, MDPI, 2023.
  • [19] S. Mubeen, R. Rahman, K. S. Nisar, J. Choi, and M. Arshad, An  extended beta function and its properties, Far  East J. Math Sci. (FJMS), 102(7) (2017), 1545–1557.
  • [20] E. O¨ zergin, M. A. O¨ zarslan, and A. Altın,  Extension  of  gamma,  beta  and  hypergeometric  functions, J. Comput. Appl. Math., 235 (2011), 4601–4610.
  • [21] R. K. Parmar, A new generalization of gamma, beta, hypergeometric and confluent hypergeometric functions, Le Matematiche, 68 (2013), 33–52.
  • [22] P. I. Pucheta, An new extended beta function, Inter. J. Math. Appl., 5(3-C) (2017), 255–260.
  • [23] G. Rahman, G. Kanwal, K. S. Nisar, and A. Ghaffar, A new extension of  beta  and  hypergeometric  functions,  (2018), 1–16. doi:10.20944/preprints201801.0074.v1
  • [24] G. Rahman, S. Mubeen, and K. S. Nisar, A new generalization of extended beta and hypergeometric functions, J. Frac. Calc. Appl., 11(2) (2020), 32–44.
  • [25] M. Shadab, J. Saime, and J. Choi, An extended beta function and its applications, J. Math. Sci., 103 (2018), 235–251.
  • [26] M. Sharma and R. Jain, A note on a generalized M-series as a special function of fractional calculus, Frac. Calc. Appl. Anal., 12(4) (2009), 449–452.
  • [27] I. N. Sneddon, Special functions of mathematical physics and chemistry, Longman Mathematical Texts, 1980.
  • [28] H. M. Srivastava, P. Agarwal, and S. Jain, Generating functions for the generalized Gauss hypergeometric func- tions, Appl. Math. Comput., 247 (2014), 348–352.
  • [29] R.  S¸ahin,  O.  Ya˘gcı,  M.  B.  Ya˘gbasan,  I˙.  O.  Kıymaz,  and  A.  C¸ etinkaya,  Further  generalizations  of  gamma,  beta and related functions, J. Ineq. Spec. Func., 9(4) (2018), 1–7.
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