Boundary value problem for p−Laplacian Caputo fractional difference equations with fractional sum boundary conditions |
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| Authors: | Thanin Sitthiwirattham |
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| Affiliation: | Nonlinear Dynamic Analysis Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology, Bangkok, Thailand |
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| Abstract: | In this paper, we consider a discrete fractional boundary value problem of the form ![urn:x-wiley:mma:media:mma3586:mma3586-math-0001]( "urn:x-wiley:mma:media:mma3586:mma3586-math-0001") where 0 < α,β≤1, 1 < α + β≤2, 0 < γ≤1,  , ρ is a constant,  and  denote the Caputo fractional differences of order α and β, respectively,  is a continuous function, and ?p is the p‐Laplacian operator. The existence of at least one solution is proved by using Banach fixed point theorem and Schaefer's fixed point theorem. Some illustrative examples are also presented. Copyright © 2015 John Wiley & Sons, Ltd. |
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| Keywords: | fractional difference equation boundary value problem existence fixed point theorems |
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