On Separate Fractional Sum-Difference Equations with n -Point Fractional Sum-Difference Boundary Conditions via Arbitrary Different Fractional Orders

Saowaluck Chasreechai and Thanin Sitthiwirattham
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Saowaluck Chasreechai: Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
Thanin Sitthiwirattham: Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok 10700, Thailand

Mathematics, 2019, vol. 7, issue 5, 1-16

Abstract: In this article, we study the existence and uniqueness results for a separate nonlinear Caputo fractional sum-difference equation with fractional difference boundary conditions by using the Banach contraction principle and the Schauder’s fixed point theorem. Our problem contains two nonlinear functions involving fractional difference and fractional sum. Moreover, our problem contains different orders in n + 1 fractional differences and m + 1 fractional sums. Finally, we present an illustrative example.

Keywords: fractional sum-difference equations; boundary value problem; existence; uniqueness (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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