Solvability of nonlinear Langevin equation involving two fractional orders with Dirichlet boundary conditions.

Ahmad, Bashir; Nieto, Juan J.

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Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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In this paper, generalized boundary value problems for nonlinear fractional Langevin equations is studied. Some new existence results of solutions in the balls with different radius are obtained when the nonlinear term satisfies nonlinear Lipschitz and linear growth conditions. Finally, two examples are given to illustrate the results.