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Upper and lower solutions method for impulsive partial hyperbolic differential equations with fractional order. (English) Zbl 1202.35340
Summary: We investigate the existence of solutions for a class of initial value problems for impulsive partial hyperbolic differential equations involving the Caputo fractional derivative by using the lower and upper solutions method combined with Schauder’s fixed point theorem.
MSC:
35R12Impulsive partial differential equations
35R11Fractional partial differential equations
26A33Fractional derivatives and integrals (real functions)
35A15Variational methods (PDE)
35A01Existence problems for PDE: global existence, local existence, non-existence