Journal
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
Volume 42, Issue 4, Pages 1151-1166Publisher
WILEY
DOI: 10.1002/mma.5419
Keywords
beta-Ulam-Hyers-Rassias stability; integrable impulse of fractional type; Lipschitz condition; Picard operator
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In this paper, we interrogate different Ulam type stabilities, ie, beta-Ulam-Hyers stability, generalized beta-Ulam-Hyers stability, beta-Ulam-Hyers-Rassias stability, and generalized beta-Ulam-Hyers-Rassias stability, for nth order nonlinear differential equations with integrable impulses of fractional type. The existence and uniqueness of solutions are investigated by using the Banach contraction principle. In the end, we give an example to support our main result.
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