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

Author(s):

Mohsen Khaleghi Moghdam *

Message:
Article Type:
Research/Original Article (بدون رتبه معتبر)
Abstract:
In this paper, we deal with the existence of a positive solution for the following fractional discrete boundary-value problemT+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:

Discrete Fractional Calculus , Discrete Nonlinear Boundary Value Problem , Non Trivial Solution , Variational Methods , Critical Point Theory

Language:
English
Published:
Global Analysis and Discrete Mathematics, Volume:8 Issue: 1, Summer and Autumn 2023
Pages:
11 to 21
https://magiran.com/p2761539