A study of the existence and uniqueness of solutions for some classes of FPDEs - Ouagueni Nora (université de msila, 2023)
In this thesis, we provide some existence and uniqueness results of solutions in Banach space, for nonlinear mixed fractional differential equations (FDEs) with two different fractional derivatives and for nonlinear fractional partial differential equations (FPDEs) involving the generalized Riesz–Caputo fractional derivative (GRCFD) respectively, both with boundary conditions. We use the Banach's contraction principle, Schauder's and Schaefer's fixed point theorems, and the technique of the nonlinear alternative of Leray-Schauder type. We also derive the self-similar solutions in an explicit form of space-time fractional diffusion equation involving Hilfer- Katugampola's fractional derivative (HKFD) by applying the successive approximation method .
Keywords: Boundary value problems (BVPs), fractional differential equations (FDEs), fractional partial differential equations (FPDEs), self similar solutions, successive approximation method, fixed point theorem, Banach space, existence, uniqueness, Ulam-Hyers stability, Katugampola's and Caputo-type Katugampola's fractional derivatives, Hilfer-Katugampola's fractional derivative