Existence and Ulam stability of initial value problem for fractional perturbed functional q-difference equations
DOI:
https://doi.org/10.24193/subbmath.2024.3.02Keywords:
Initial value problem, Caputo fractional q-derivative, Burton and Kirk’s fixed point theorem, Ulam-Hyers stability, Ulam-Hyers-Rassias stabilityAbstract
In this work, we discuss the existence and uniqueness of solutions to the initial value problem for perturbed functional fractional q-difference equations involving q-derivative of the Caputo sense. By applying Banach contraction principle and Burton and Kirk’s fixed-point theorems. Further, we present the Ulam-Hyers and Ulam-Hyers-Rassias stabilities results by using direct analysis methods. Finally, we give two examples illustrating the results.
Mathematics Subject Classification (2010): 26A33, 34A12, 39A13, 47H10.
Received 15 March 2022; Accepted 12 September 2022.
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