A Survey on Existence of a Solution to Singular Fractional Difference Equation

Document Type : Research Paper

Author

Department of Basic Sciences, Sari Agricultural Sciences and Natural Resources University, Sari, Iran

Abstract

In this paper, we deal with the existence of a positive solution for the following fractional discrete boundary-value problem
T+1∇αk(k∇α0(UK)))=λƒ(K,U(K)), k∈[1,T]N0,
u(0)=u (T+1)=0,

where 0<α<1 and k∇α0 is the left nabla discrete fractional difference and T+1∇αk is the right nabla discrete fractional difference ƒ:[1,T]N0×(0,+∞)→R may be singular at t=0  and may change sign and λ>0 is a parameter. The technical method is variational approach for differentiable functionals. An example is included to illustrate the main results.

Keywords

Global Analysis and Discrete Mathematics
Volume 8, Issue 1
November 2023
Pages 11-21

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History

  • Receive Date: 20 December 2023
  • Revise Date: 04 February 2024
  • Accept Date: 05 February 2024

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