The difference between a class of discrete fractional and integer order boundary value problems |
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| Institution: | 1. Department of Mathematics, China University of Mining and Technology, Xuzhou 221116, PR China;2. School of Mathematics and Statistics, Central South University, Changsha, Hunan 410083, PR China;1. College of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, PR China;2. Department of Information Technology, Hunan Women’s University, Changsha, Hunan 410004, PR China;1. Department of Mathematics, Linyi University, Linyi, Shandong 276005, PR China;2. Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt |
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| Abstract: | In this paper, we point out the differences between a class of fractional difference equations and the integer-order ones. We show that under the same boundary conditions, the problem of the fractional order is nonresonant, while the integer-order one is resonant. Then we analyse the discrete fractional boundary value problem in detail. Then the uniqueness and multiplicity of the solutions for the discrete fractional boundary value problem are obtained by two new tools established in 2012, respectively. |
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| Keywords: | Fractional order Discrete fractional boundary value problems Fractional difference equations |
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