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Existence and asymptotic behaviors of nonlinear neutral Caputo nabla fractional difference equations

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Abstract

In this paper, we consider a nonlinear neutral Caputo nabla fractional difference equation. In the analysis, we use the nabla discrete Mittag–Leffler functions to transform the equation into an applicable equation. By applying Krasnoselskii’s fixed point theorem, sufficient conditions for the existence of solutions are established, also the uniqueness of the solution is given by the Contraction mapping principle. In addition, we give interesting results for stability and asymptotic stability. To examine the validity of our findings, a concrete example with numerical simulation diagrams is analyzed. Our main results extend and generalize the results that are obtained in [12].

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, University of Ha’il, Ha’il, 2440, Saudi Arabia

    Mouataz Billah Mesmouli & Naveed Iqbal

  2. Department of Mathematics and Informatics, University of Souk Ahras, P.O. Box 1553, Souk Ahras, 41000, Algeria

    Abdelouaheb Ardjouni

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  1. Mouataz Billah Mesmouli
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  2. Abdelouaheb Ardjouni
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  3. Naveed Iqbal
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Correspondence to Mouataz Billah Mesmouli.

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Mesmouli, M.B., Ardjouni, A. & Iqbal, N. Existence and asymptotic behaviors of nonlinear neutral Caputo nabla fractional difference equations. Afr. Mat. 33, 83 (2022). https://doi.org/10.1007/s13370-022-01020-w

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