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Generalized boundary value problems for nonlinear fractional Langevin equations. (English) Zbl 1318.34008
The authors study existence results for generalized boundary value problems for nonlinear fractional Langevin equations. The proof is based on the well-known Banach’s contraction mapping principle, Krasnoselskii’s fixed point theorem and the nonlinear contraction mapping.
Their work improve earlier results: (i) the boundary conditions fit more physical measurements; (ii) the nonlinear term satisfies a nonlinear D-contraction and linear growth conditions; (iii) their assumptions are weakened and easy to check.
Finally, they give several examples to illustrate their main result.
MSC:
34A08 Fractional ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
47N20 Applications of operator theory to differential and integral equations
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