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Volume 10, Number 6, 2020, Pages 2557-2574                                                                DOI:10.11948/20190419
Existence results of solutions for anti-periodic fractional Langevin equation
Ahmed Salem
Keywords:Existence solution, fractional Langevin equation, anti-periodic condition.
Abstract:
      Recently, Khalili and Yadollahzadeh [ Y. Khalili and M. Yadollahzadeh, Existence results for a new class of nonlinear Langevin equations of fractional orders, Iranian J. Sci. Tech., Trans. A: Sci., 2019, 43(5), 2335–2342] have investigated the uniqueness and existence of solution $u(t),~t\in[0,1]$ for a class of nonlocal boundary conditions to fractional Langevin equation. The authors used the boundary condition $u""(0)=0$ by incorrect method. In the current contribution, we show the correct method for using this condition and study the existence and uniqueness of solution for the same class of equation in slightly different form with anti-periodic and nonlocal integral boundary conditions as well as the boundary condition $u""(0)=0$. An exemplar is provided to illustrate our results.
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