ULAM-HYERS-RASSIAS STABILITY AND EXISTENCE OF SOLUTIONS TO NONLINEAR FRACTIONAL DIFFERENCE EQUATIONS WITH MULTIPOINT SUMMATION BOUNDARY CONDITION

doi:10.1007/s10473-020-0219-1

Abstract

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 μ∈ (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.

Key words: Fractional difference equation, Green's function, existence and uniqueness, Ulam-Hyers-Rassias stability, summation boundary condition

CLC Number:

39A30

Syed Sabyel HAIDER, Mujeeb Ur REHMAN. ULAM-HYERS-RASSIAS STABILITY AND EXISTENCE OF SOLUTIONS TO NONLINEAR FRACTIONAL DIFFERENCE EQUATIONS WITH MULTIPOINT SUMMATION BOUNDARY CONDITION[J].Acta mathematica scientia,Series B, 2020, 40(2): 589-602.

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