On the Existence of Solution for a Sum Fractional Finite Difference Inclusion

  • Vahid Ghorbanian
  • Shahram RezapourEmail author
  • Saeid Salehi
Part of the Nonlinear Systems and Complexity book series (NSCH, volume 23)


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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© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • Vahid Ghorbanian
    • 1
  • Shahram Rezapour
    • 1
    Email author
  • Saeid Salehi
    • 1
  1. 1.Department of MathematicsAzarbaijan Shahid Madani UniversityTabrizIran

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