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Analysis of fractional-order functional differential equations with multiple delays

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FD2W01 - Deterministic and stochastic fractional diļ¬€erential equations and jump processes

In this reserach work, we consider an initial value problem for a linear matrix coefficients system of fractional-order differential equations with multiple constant delays in the sense of Caputo. First, we derive anexplicit analytical solution for linear inhomogeneous fractional multi-delay differential equations of order0 < α < 1. The obtained results are covering the corresponding results for first-order differential systemswith multiple constant delays. Second, we prove the global existence and uniqueness of the solution of anonlinear time-delay system with fractional-order using the principle of contraction mapping in a weightedspace of continuous functions. We analyze finite-time stability for a class of fractional-order differentialequations with multiple delays. We derive some sufficient conditions for the finite-time stability based ona multi-delayed perturbation of the Mittag-Leffler type matrix function by virtue of Gronwall’s integralinequality. Finally, we demonstrate the validity of the developed technique and discuss it with numericalexamples.

This talk is part of the Isaac Newton Institute Seminar Series series.

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