Finite-Time Stability in Nonhomogeneous Delay Differential Equations of Fractional Hilfer Type

Ahmed Salem and Rawia Babusail
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Ahmed Salem: Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
Rawia Babusail: Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Mathematics, 2022, vol. 10, issue 9, 1-14

Abstract: In the current contribution, integral representations of the solutions of homogeneous and nonhomogeneous delay differential equation of a fractional Hilfer derivative are established in terms of the delayed Mittag-Leffler-type matrix function of two parameters. By using the method of variation of constants, the solution representations are represented. Finite-time stability of the solutions is examined with provision of appropriate sufficient conditions. Finally, an illustrated numerical example is introduced to apply the theoretical results.

Keywords: finite-time stability; Hilfer derivative; linear fractional delay differential equation; delayed Mittag-Leffler type matrix of two parameters (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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