On ψ-quantum fractional operators: Existence, uniqueness and Ulam-Hyers stability
1International Program in Business Law (LL.B.), Faculty of Law, Thammasat University, Phra Barom Maha Ratchawang, Phra Nakhon, Bangkok, 10200, Thailand
2Department of Mathematics, Sule Lamido University, Kafin Hausa, P.M.B 048 Kafin Hausa, Jigawa State, 700271, Nigeria
2Department of Mathematics, Sule Lamido University, Kafin Hausa, P.M.B 048 Kafin Hausa, Jigawa State, 700271, Nigeria
Sigma J Eng Nat Sci 2024; 42(2): 313-320 DOI: 10.14744/sigma.2024.00034
Abstract
In this paper, we study the generalized concept of q-calculus with respect to another func-tion. The 𝜓-quantum Riemann-Liouville fractional integral, 𝜓-quantum Riemann-Liouville fractional derivative, and 𝜓-quantum Caputo fractional derivative were introduced. The ex-istence, uniqueness, and Ulam-Hyers stability of the solutions with the mentioned derivatives were established. Finally, some examples are considered to demonstrate the results obtained.
Keywords: Q-Calculus; ψ-Quantum; Ulam-Hyers Stability; Banach Contraction
