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Ulam-Hyers-Rassias Stability and Existence of Solutions to Nonlinear Fractional Difference Equations with Multipoint Summation Boundary Condition

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Abstract

The purpose of this study is to acquire some conditions that reveal existence and stability for solutions to a class of difference equations with non-integer order ώ ∈ (1, 2]. The required conditions are obtained by applying the technique of contraction principle for uniqueness and Schauder’s fixed point theorem for existence. Also, we establish some conditions under which the solution of the considered class of difference equations is generalized Ulam-Hyers-Rassias stable. Example for the illustration of results is given.

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Authors and Affiliations

  1. School of Natural Sciences, National University of Sciences and Technology, H-12, Islamabad, 44000, Pakistan

    Syed Sabyel Haider & Mujeeb Ur Rehman

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  1. Syed Sabyel Haider
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  2. Mujeeb Ur Rehman
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Correspondence to Syed Sabyel Haider.

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Haider, S.S., Rehman, M.U. Ulam-Hyers-Rassias Stability and Existence of Solutions to Nonlinear Fractional Difference Equations with Multipoint Summation Boundary Condition. Acta Math Sci 40, 589–602 (2020). https://doi.org/10.1007/s10473-020-0219-1

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  • DOI: https://doi.org/10.1007/s10473-020-0219-1

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