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

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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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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Keywords

  • Fractional difference equations
  • Fixed point theorem
  • Arzela-Ascoli’s theorem
  • Nabla discrete Mittag–Leffler functions

Mathematics Subject Classification

  • 34K20
  • 26A33
  • 47H10