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Exploring delayed Mittag-Leffler type matrix functions to study finite time stability of fractional delay differential equations

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  • Li, Mengmeng
  • Wang, JinRong

Abstract

In this paper, we introduce a concept of delayed two parameters Mittag-Leffler type matrix function, which is an extension of the classical Mittag-Leffler matrix function. With the help of the delayed two parameters Mittag-Leffler type matrix function, we give an explicit formula of solutions to linear nonhomogeneous fractional delay differential equations via the variation of constants method. In addition, we prove the existence and uniqueness of solutions to nonlinear fractional delay differential equations. Thereafter, we present finite time stability results of nonlinear fractional delay differential equations under mild conditions on nonlinear term. Finally, an example is presented to illustrate the validity of the main theorems.

Suggested Citation

  • Li, Mengmeng & Wang, JinRong, 2018. "Exploring delayed Mittag-Leffler type matrix functions to study finite time stability of fractional delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 324(C), pages 254-265.
    • Handle: RePEc:eee:apmaco:v:324:y:2018:i:c:p:254-265
    DOI: 10.1016/j.amc.2017.11.063
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    References listed on IDEAS

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    1. Gautam, Ganga Ram & Dabas, Jaydev, 2015. "Mild solutions for class of neutral fractional functional differential equations with not instantaneous impulses," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 480-489.
    2. Abbas, Saïd & Benchohra, Mouffak, 2015. "Uniqueness and Ulam stabilities results for partial fractional differential equations with not instantaneous impulses," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 190-198.
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