Uniqueness of continuous solution to $q$-Hilfer fractional hybrid integro-difference equation of variable order

https://doi.org/10.48185/jmam.v2i3.421

Authors

  • IDRIS AHMED Sule Lamido University, Kafin Hausa, P.M.B 048 Kafin Hausa
  • Norravich Limpanukorn International Program in Business Law (LL.B.), Faculty of Law, Thammasat University, Thailand
  • Muhammad Jamilu Ibrahim International Program in Business Law (LL.B.), Faculty of Law, Thammasat University, Thailand

Keywords:

$q$-calculus, Hilfer fractional derivative, Hybrid integro-difference equation, Variable-order

Abstract

In this paper, the authors introduced a novel definition based on Hilfer fractional derivative, which name $q$-Hilfer fractional derivative of variable order. And the uniqueness of solution to $q$-Hilfer fractional hybrid integro-difference equation of variable order of the form \eqref{eq:varorderfrac} with $0 < \alpha(t) < 1$, $0 \leq \beta \leq 1$, and $0 < q < 1$ is studied. Moreover, an example is provided to demonstrate the result.

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Author Biography

IDRIS AHMED, Sule Lamido University, Kafin Hausa, P.M.B 048 Kafin Hausa

IDRIS AHMED was born in Gumel Local Government, Jigawa state, Nigeria on 13th January 1988. He received the B.S. and M.S. degrees in mathematics from the Bayero University Kano, Kano Nigeria, respectively, in 2010 and 2017. He obtained his Ph. D in Applied Mathematics from King Mongkut's University of Technology Thonburi, Thailand. At present, he is a lecturer II with the Department of Mathematics and Computer Science, Faculty of Natural and Applied Sciences, Sule Lamido University Kafin Hausa.

Published

2021-12-30

How to Cite

AHMED, I., Limpanukorn, N. ., & Ibrahim, M. J. . (2021). Uniqueness of continuous solution to $q$-Hilfer fractional hybrid integro-difference equation of variable order. Journal of Mathematical Analysis and Modeling, 2(3), 88–98. https://doi.org/10.48185/jmam.v2i3.421

Issue

Vol. 2 No. 3 (2021): 2021 (3)

Section

Articles
Copyright & Licensing

Copyright (c) 2021 IDRIS AHMED, Norravich Limpanukorn, Muhammad Jamilu Ibrahim

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.