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.


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
Full Text: EMIS