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Construction of exact solutions for fractional order differential equations by the invariant subspace method. (English) Zbl 1348.34012

Summary: The invariant subspace method for constructing particular solutions is modified for fractional differential equations. It allows one to reduce a fractional partial differential equation to a system of nonlinear ordinary fractional differential equations. Point symmetries of such systems are used to construct their solutions which generate solutions of the original fractional partial differential equation.

MSC:

34A08 Fractional ordinary differential equations
34C14 Symmetries, invariants of ordinary differential equations
34A05 Explicit solutions, first integrals of ordinary differential equations
35R11 Fractional partial differential equations
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References:

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