Special functions with general kernel: Properties and applications to fractional partial differential equations
By: Enes Ata and İsmail Onur Kıymaz
References
- Baleanu D., Diethelm K., Scalas E., Trujillo J.J., Fractional Calculus: Models and Numerical Methods, World Scientific, London, 2012.
- Hilfer R., Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000.
- Miller K.S., Ross B., An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, USA, 1993.
- Samko S.G., Kilbas A.A., Marichev O.I., Fractional Integrals and Derivatives: Theory and Applications, Gordon, Breach Science Publication, 1993.
- Podlubny I., Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications, Academic Press, 1999.
- Kilbas A.A., Srivastava H.M., Trujillo J.J., Theory and Applications of Fractional Differential, North-Holland Mathematics Studies, 204, 2006.
- Tanriverdi T., Baskonus H.M., Mahmud A.A., Muhamad K.A., Explicit solution of fractional order atmosphere-soil-land plant carbon cycle system, Ecological Complexity, 48, 100966, 2021.
- Ata E., Kıymaz İ.O., A new generalized Laplace transform and its applications to fractional Bagley-Torvik and fractional harmonic vibration problems, Miskolc Mathematical Notes, 24(2), 597–610, 2023.
- Luchko Y.F., Martinez H., Trujillo J.J., Fractional fourier transform and some of its applications, Fractional Calculus and Applied Analysis, 11(4), 457–470, 2008.
- Ata E., Kıymaz İ.O., New generalized Mellin transform and applications to partial and fractional differential equations, International Journal of Mathematics and Computer in Engineering, 1(1), 45–66, 2023.
- Lin S.D., Lu C.H., Laplace transform for solving some families of fractional differential equations and its applications, Advances in Difference Equations, 2013(1), 1–9, 2013.
- Andrews G.E., Askey R., Roy R., Special Functions, Cambridge University Press, Cambridge, 1999.
- Parmar R.K., A new generalization of gamma, beta, hypergeometric and confluent hypergeometric functions, Le Matematiche, 68, 33–52, 2013.
- Şahin R., Yağcı O., Yağbasan M.B., Kıymaz İ.O., Çetinkaya A., Further generalizations of gamma, beta and related functions, Journal of Inequalities and Special Functions, 9(4), 1–7, 2018.
- Khan N., Husain S., A note on extended beta function involving generalized Mittag-Leffler function and its applications, TWMS Journal of Applied and Engineering Mathematics, 12(1), 71–81, 2022.
- Çetinkaya A., Kıymaz İ.O., Agarwal P., Agarwal R.A., A comparative study on generating function relations for generalized hypergeometric functions via generalized fractional operators, Advances in Difference Equations, 2018(1), 1–11, 2018.
- Abubakar U.M., New generalized beta function associated with the Fox-Wright function, Journal of Fractional Calculus and Application, 12(2), 204–227, 2021.
- Abubakar U.M., A study of extended beta and associated functions connected to Fox-Wright function, Journal of Fractional Calculus and Application, 12(3)(13), 1–23, 2021.
- Al-Gonah A., Mohammed W.K., A new extension of extended Gamma and Beta functions and their properties, Journal of Scientific and Engineering Research, 5(9), 257–270, 2018.
- Ata E., Kıymaz İ.O., A study on certain properties of generalized special functions defined by Fox-Wright function, Applied Mathematics and Nonlinear Sciences, 5(1), 147–162, 2020.
- Ata E., Modified special functions defined by generalized M-series and their properties, arXiv:2201.00867v1, 2022.
- Ata E., Kıymaz İ.O., Generalized gamma, beta and hypergeometric functions defined by Wright function and applications to fractional differential equations, Cumhuriyet Science Journal, 43(4), 684–695, 2022.
- Atash A.A., Barahmah S.S., Kulib M.A., On a new extensions of extended gamma and beta functions, International Journal of Statistics and Applied Mathematics, 3(6), 14–18, 2018.
- Chaudhry M.A., Zubair S.M., Generalized incomplete gamma functions with applications, Journal of Computational and Applied Mathematics, 55, 99–124, 1994.
- Chaudhry M.A., Qadir A., Rafique M., Zubair S.M., Extension of Euler’s beta function, Journal of Computational and Applied Mathematics, 78, 19–32, 1997.
- Chaudhry M.A., Qadir A., Srivastava H.M., Paris R.B., Extended hypergeometric and confluent hypergeometric functions, Applied Mathematics and Computation, 159, 589–602, 2004.
- Choi J., Rathie A.K., Parmar R.K., Extension of extended beta, hypergeometric and confluent hypergeometric functions, Honam Mathematical Journal, 36, 357–385, 2014.
- Goswami A., Jain S., Agarwal P., Aracı S., A note on the new extended beta and Gauss hypergeometric functions, Applied Mathematics and Information Sciences, 12, 139–144, 2018.
- Goyal R., Momani S., Agarwal P., Rassias M.T., An extension of beta function by using Wiman’s function, Axioms, 10(3), 187, 2021.
- Kulip M.A.H., Mohsen F.F., Barahmah S.S., Further extended gamma and beta functions in term of generalized Wright function, Electronic Journal of University of Aden for Basic and Applied Sciences, 1(2), 78–83, 2020.
- Lee D.M., Rathie A.K., Parmar R.K., Kim Y.S., Generalization of extended beta function, hypergeometric and confluent hypergeometric functions, Honam Mathematical Journal, 33, 187–206, 2011.
- Mubeen S., Rahman R., Nisar K.S., Choi J., Arshad M., An extended beta function and its properties, Far East Journal of Mathematical Sciences, 102(7), 1545–1557, 2017.
- Özergin E., Özarslan M.A., Altın A., Extension of gamma, beta and hypergeometric functions, Journal of Computational and Applied Mathematics, 235, 4601–4610, 2011.
- Rahman G., Mubeen S., Nisar K.S., A new generalization of extended beta and hypergeometric functions, Journal of Fractional Calculus and Applications, 11(2), 32–44, 2020.
- Rahman G., Kanwal G., Nisar K.S., Ghaffar A., A new extension of beta and hypergeometric functions, Preprints, 1–16, 2018.
- Shadab M., Saima J., Choi J., An extended beta function and its applications, Far East Journal of Mathematical Sciences, 103(1), 235–251, 2018.
- Ata E., Kıymaz İ.O., 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, 12(1), 31–43, 2024.
- Srivastava H.M., Agarwal P., Jain S., Generating functions for the generalized Gauss hypergeometric functions, Applied Mathematics and Computation, 247, 348–352, 2014.
- Ata E., Generalized beta function defined by Wright function, arXiv:1803.03121v3, 2018.
- Kıymaz İ.O., Çetinkaya A., Agarwal P., An extension of Caputo fractional derivative operator and its applications, Journal of Nonlinear Sciences and Applications, 9, 3611–3621, 2016.
- Srivastava H.M., Çetinkaya A., Kıymaz İ.O., A certain generalized Pochhammer symbol and its applications to hyper-geometric functions, Applied Mathematics and Computation, 226, 484–491, 2014.
- Kıymaz İ.O., Agarwal P., Jain S., Çetinkaya A., Advances in Real and Complex Analysis with Applications (Chapter 11: On a new extension of Caputo fractional derivative operator), Birkhäuser, Switzerland, 2017.
- Debnath L., Bhatta D., Integral Transforms and Their Applications (3rd Ed.), CRC Press, USA, 2015.
- Anwar A.M.O., Jarad F., Baleanu D., Ayaz F., Fractional caputo heat equation within the double Laplace transform, Romanian Journal of Physics, 58(1–2), 15–22, 2013.
- Debnath L., The Double Laplace transforms and their properties with applications to functional, integral and partial differential equations, International Journal of Applied and Computational Mathematics, 2, 223–241, 2016.
DOI: https://doi.org/10.2478/ijmce-2025-0013 | Journal eISSN: 2956-7068
Language: English
Page range: 153 - 170
Submitted on: Oct 10, 2023
Accepted on: Feb 28, 2024
Published on: Sep 22, 2024
Published by: Harran University
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year
Keywords:
Related subjects:
© 2024 Enes Ata, İsmail Onur Kıymaz, published by Harran University
This work is licensed under the Creative Commons Attribution 4.0 License.