A new generalization of Mittag-Leffler function via q-calculus-Reference-Cited by-同舟云学术

A new generalization of Mittag-Leffler function via q-calculus

Published:2020-12 Issue:1 Volume:2020 Page:
ISSN:1687-1847
Container-title:Advances in Difference Equations
language:en
Short-container-title:Adv Differ Equ

Author:

Nadeem Raghib,Usman Talha,Nisar Kottakkaran Sooppy,Abdeljawad Thabet^ORCID

Abstract

AbstractThe present paper deals with a new different generalization of the Mittag-Leffler function through q-calculus. We then investigate its remarkable properties like convergence, recurrence relation, integral representation, q-derivative formula, q-Laplace transformation, and image formula under q-derivative operator. In addition to this, we consider some specific cases to give the utilization of our main results.

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Algebra and Number Theory,Analysis

Link

http://link.springer.com/content/pdf/10.1186/s13662-020-03157-z.pdf

Reference21 articles.

1. Abdeljawad, T., Baleanu, D.: Caputo q-fractional initial value problems and a q-analogue Mittag-Leffler function. Commun. Nonlinear Sci. Numer. Simul. 16(12), 4682–4688 (2011)

2. Abdeljawad, T., Benli, B., Baleanu, D.: A generalized q-Mittag-Leffler function by q-captuo fractional linear equations. Abstr. Appl. Anal. 2012, Article ID 546062 (2012). https://doi.org/10.1155/2012/546062

3. Agarwal, P., Chand, M., Certain, J.S.: Integrals involving generalized Mittag-Leffler functions. Proc. Natl. Acad. Sci. India Sect. A 85(3), 359–371 (2015)

4. Agarwal, R.P.: Certain fractional q-integrals and q-derivatives. Math. Proc. Camb. Philos. Soc. 66, 365–370 (1969)

5. Garg, M., Chanchlani, L.: Kober fractional q-derivative operators. Matematiche 66(1), 13–26 (2011)

Cited by 6 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. On the fractional q-integral operators involving q-analogue of Mittag-Leffler function;Analysis;2024-04-24

2. On Saigo Fractional q-Calculus of a General Class of q-Polynomials;SAHAND COMMUN MATH A;2024

3. Solutions to Fractional q-Kinetic Equations Involving Quantum Extensions of Generalized Hyper Mittag-Leffler Functions;Fractal and Fractional;2024-01-16

4. The Prabhakar Fractional q-Integral and q-Differential Operators;Trends in Mathematics;2024

5. On the Riemann–Liouville fractional q -calculus operator involving q -Mittag–Leffler function;Research in Mathematics;2023-12-14