STUDY OF FRACTIONAL ORDER DELAY CAUCHY NON-AUTONOMOUS EVOLUTION PROBLEMS VIA DEGREE THEORY

Zareen A. Khan (), Kamal Shah, Ibrahim Mahariq () and Hussam Alrabaiah ()
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Zareen A. Khan: Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia
Kamal Shah: Department of Mathematics, University of Malakand, Chakdara Dir (L), 18000 Khyber Pakhtunkhwa, Pakistan3Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, Saudi Arabia
Ibrahim Mahariq: College of Engineering and Technology, American University of the Middle East, Kuwait
Hussam Alrabaiah: Department of Mathematics, Tafila Technical University, Tafila, Jordan, College of Engineering, Al Ain University, Al Ain, United Arab Emirates

FRACTALS (fractals), 2022, vol. 30, issue 01, 1-12

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.

Keywords: Non-Autonomous Evolution Problem; Cauchy Problem; TDM; Stability (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22400138

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