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Existence of nonlinear Lane-Emden equation of fractional order. (English) Zbl 1265.34216
Summary: We study a Dirichlet boundary value problem for the Lane-Emden equation involving two fractional orders. Recently, a new type of Lane-Emden equation with two different fractional orders has been introduced which provides a more flexible model for fractal processes. The contraction mapping principle and Krasnosel’skii’s fixed point theorem are applied to prove the existence of solutions of the problem in a Banach space.

34G20 Nonlinear differential equations in abstract spaces
34A08 Fractional ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations