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Non-local problems with integral gluing condition for loaded mixed type equations involving the Caputo fractional derivative. (English) Zbl 1383.35239

Summary: In this work, we study the existence and uniqueness of solutions to non-local boundary value problems with integral gluing condition. Mixed type equations (parabolic-hyperbolic) involving the Caputo fractional derivative have loaded parts in Riemann-Liouville integrals. Thus we use the method of integral energy to prove uniqueness, and the method of integral equations to prove existence.

MSC:

35R11 Fractional partial differential equations
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
35C05 Solutions to PDEs in closed form
35C15 Integral representations of solutions to PDEs
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