Abstract
By using a recent fixed point result for α-admissible α-Ψ multifunctions, we investigate the existence of solutions for the fractional finite difference inclusion \(\varDelta _{\nu -2}^\nu x(t)+\varDelta _{\nu -2}^{\nu -1} x(t)+\varDelta _{\nu -2}^{\nu -2} x(t+1)\in F\big (t,x(t),\varDelta x(t),\varDelta ^2 x(t),\varDelta ^\mu x(t),\varDelta ^\gamma x(t)\big )\) with the boundary conditions x(ν) = 0 and x(ν + b + 2) = 0, where 1 < γ ≤ 2, 0 < μ ≤ 1, 3 < ν ≤ 4 and \(F:\mathbb {N}_{\nu -2}^{b+\nu }\times \mathbb {R}^5\to 2^{\mathbb {R}} \) is a compact valued multifunction.
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Ghorbanian, V., Rezapour, S., Salehi, S. (2019). On the Existence of Solution for a Sum Fractional Finite Difference Inclusion. In: Taş, K., Baleanu, D., Machado, J. (eds) Mathematical Methods in Engineering. Nonlinear Systems and Complexity, vol 23. Springer, Cham. https://doi.org/10.1007/978-3-319-91065-9_7
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