On ψ-quantum fractional operators: Existence, uniqueness and Ulam-Hyers stability

Year 2024, Volume: 42 Issue: 2, 313 - 320, 30.04.2024

Norravich Limpanukorn Idris Ahmed , Muhammad Jamilu Ibrahim

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

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