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- Title
STUDY OF FRACTIONAL ORDER DELAY CAUCHY NON-AUTONOMOUS EVOLUTION PROBLEMS VIA DEGREE THEORY.
- Authors
KHAN, ZAREEN A.; SHAH, KAMAL; MAHARIQ, IBRAHIM; ALRABAIAH, HUSSAM
- Abstract
This work is devoted to derive some existence and uniqueness (EU) conditions for the solution to a class of nonlinear delay non-autonomous integro-differential Cauchy evolution problems (CEPs) under Caputo derivative of fractional order. The required results are derived via topological degree method (TDM). TDM is a powerful tool which relaxes strong compact conditions by some weaker ones. Hence, we establish the EU under the situation that the nonlinear function satisfies some appropriate local growth condition as well as of non-compactness measure condition. Furthermore, some results are established for Hyers–Ulam (HU) and generalized HU (GHU) stability. Our results generalize some previous results. At the end, by a pertinent example, the results are verified.
- Subjects
TOPOLOGICAL degree; DELAY differential equations; CAPUTO fractional derivatives; CAUCHY problem; NONLINEAR functions
- Publication
Fractals, 2022, Vol 30, Issue 1, p1
- ISSN
0218-348X
- Publication type
Article
- DOI
10.1142/S0218348X22400138