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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 \cite{ky} investigated the uniqueness and existence of solution $u(t),~t\in[0,1]$ for class of nonlocal boundary conditions to 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.