Study of fractional Caputo derivatives operator by symmetric kernel
Resumo
The current study investigates the new type of Caputo fractional derivative operator with a symmetric kernel. We also examine some important properties related to this new type of Caputo fractional derivative operator.
Downloads
Referências
Kilbas, A.A., Srivastava H.M., Trujillo, J.J. Theory and applications of fractional differential equations, Elsevier Science B.V., Amsterdam, 2006.
Agarwal, P., Baleanu, D., Chen, Y., Momani, M.S. Fractional Calculus, ICFDA 2018, Amman, Jordan, July 16–18. Proceedings in Mathematics and Statistics. Springer, Berlin 2019.
Goyal, R.; Agarwal, P.; Parmentier, A.; Cesarano, C. An Extension of Caputo Fractional Derivative Operator by Use of Wiman’s Function. Symmetry 2021, 13, 2238.
Kiyamaz, I.O., Cetinkaya A., Agarwal P. An extension of Caputo fractional derivative operator and its applications, J. Nonlinear Sci. Appl. 2016, 9, 3611–3621.
Wiman A. Uber die Nullstellun der Funktionen Eα(x). Acta Mathematica. 1905, 29, 217–234.
Gorenflo R., Kilbas A.A., Mainardi F., Rogosin S.V. Mittage Leffler Functions Related Topics and Application, 2nd ed.; Springer: New York, NY, USA, 2020.
Rainville E.D. Special Functions, Macmillan, New York, NY, USA, 1960.
Goyal R., Agarwal P., Momami S., Rassias M.T. An Extension of Beta Function by Using Wiman’s Function. Axioms.bf 2021, 10, 187.
Olver W.J.F., Lozier W.D., Boisvert F.R., Clark W.C. NIST Handbook of Mathematical Functions, Cambridge University Press, New York, NY, USA, 2010.
Prabhakar T.R. A singular integral equation with a generalized Mittag-Leffler function in the kernel. Yokohama Mathematical Journal. 1971, 19, 7–15.
Mittag-Leffler G.M. Sur la nouvelle fonction Eα(x). Comptes rendus de l’Academie des Sciences.1903, 137, 554–558.
Srivastava H.M., Manocha H.L. A treatise on generating functions, Ellis Horwood Limited, Chichester, 1984.
Gerhold S. Asymptotics for a varient of the Mittag-Leffler function. Int. Trans. Spec. Func. 2012, 23(6), 397–403.
Copyright (c) 2025 Boletim da Sociedade Paranaense de Matemática
This work is licensed under a Creative Commons Attribution 4.0 International License.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
