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

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.