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

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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