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

1
Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
2
Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok 10700, Thailand
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(5), 471; https://doi.org/10.3390/math7050471
Received: 7 May 2019 / Revised: 17 May 2019 / Accepted: 20 May 2019 / Published: 24 May 2019
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PDF [320 KB, uploaded 29 May 2019]

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. View Full-Text
Keywords: fractional sum-difference equations; boundary value problem; existence; uniqueness fractional sum-difference equations; boundary value problem; existence; uniqueness
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Chasreechai, S.; Sitthiwirattham, T. On Separate Fractional Sum-Difference Equations with n-Point Fractional Sum-Difference Boundary Conditions via Arbitrary Different Fractional Orders. Mathematics 2019, 7, 471.

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