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Generalized Proportional Caputo Fractional Differential Equations with Noninstantaneous Impulses: Concepts, Integral Representations, and Ulam-Type Stability

Author

Listed:
  • Ravi Agarwal

    (Department of Mathematics, Texas A&M University-Kingsville, Kingsville, TX 78363, USA)

  • Snezhana Hristova

    (Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 4000 Plovdiv, Bulgaria)

  • Donal O’Regan

    (School of Mathematical and Statistical Sciences, National University of Ireland, H91 TK33 Galway, Ireland)

Abstract

The generalized proportional Caputo fractional derivative is a comparatively new type of derivative that is a generalization of the classical Caputo fractional derivative, and it gives more opportunities to adequately model complex phenomena in physics, chemistry, biology, etc. In this paper, the presence of noninstantaneous impulses in differential equations with generalized proportional Caputo fractional derivatives is discussed. Generalized proportional Caputo fractional derivatives with fixed lower limits at the initial time as well as generalized proportional Caputo fractional derivatives with changeable lower limits at each impulsive time are considered. The statements of the problems in both cases are set up and the integral representation of the solution of the defined problem in each case is presented. Ulam-type stability is also investigated and some examples are given illustrating these concepts.

Suggested Citation

  • Ravi Agarwal & Snezhana Hristova & Donal O’Regan, 2022. "Generalized Proportional Caputo Fractional Differential Equations with Noninstantaneous Impulses: Concepts, Integral Representations, and Ulam-Type Stability," Mathematics, MDPI, vol. 10(13), pages 1-26, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:13:p:2315-:d:854250
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    Cited by:

    1. Shahram Rezapour & Sina Etemad & Ravi P. Agarwal & Kamsing Nonlaopon, 2022. "On a Lyapunov-Type Inequality for Control of a ψ -Model Thermostat and the Existence of Its Solutions," Mathematics, MDPI, vol. 10(21), pages 1-11, October.

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