Abstract
This paper is devoted to seeking the representation of solutions to a linear fractional delay differential equation of Hadamard type. By introducing the Mittag-Leffler delay matrix functions with logarithmic functions and analyzing their properties, we derive the representation of solutions via the constant variation method.
Highlights
1 Introduction In the recent decades, fractional differential equations have been applied in engineering, physics, finance, and signal analysis
The researchers focused on the investigation of the existence, asymptotic stability, and finite-time stability of solutions of fractional linear and non-linear differential equations of Caputo type, Riemann–Liouville type, and Hadamard type [1,2,3,4,5,6,7,8,9,10,11]
Klusainov and Shukin [12], Diblik and Klusainov [13, 14] derived the exact expressions of solutions of linear time invariant continuous and discrete delay equations by proposing the concepts of delay matrix functions
Summary
Fractional differential equations have been applied in engineering, physics, finance, and signal analysis. The representation of solutions to delay differential equations has been considered. Klusainov and Shukin [12], Diblik and Klusainov [13, 14] derived the exact expressions of solutions of linear time invariant continuous and discrete delay equations by proposing the concepts of delay matrix functions.
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