Existence Of Solutions To Several Classes Of Boundary Value Problems Of Fractional Differential Equations At Resonance

By applying coincidence degree, this dissertation deals with the existence of solution, the unique solution and positive solutions of boundary value problems for fractional differential equations at resonance.Firstly, we present the existence of solutions of boundary value problems for a higher-order fractional differential equations with the Caputo fractional derivative at resonance by coincidence degree. Furthermore, we establish the existence and uniqueness of solutions for boundary value problems of a coupled fractional differential equations at resonance by contin-uation theorem. By the Leggett-Williams theorem for coincidences of multi-valued operators due to O’Regan and Zima, we obtain the existence of positive solutions for a class of fractional differential inclusion with boundary value conditions at resonance.Secondly, we discuss the existence of solutions of integral boundary conditions for frac-tional differential equations with the Caputo fractional derivative at resonance. By coincidence degree, we present the existence of solutions of integral boundary conditions for fractional d-ifferential equations with higher-order Riemann-Liouville fractional derivative at resonance. We study the existence of positive solutions for fractional differential equations with integral boundary conditions by the Leggett-Williams norm-type theorem for coincidences.Finally, we investigate the existence result for nonlinear fractional differential equation with p-Laplacian operator at resonance. At the beginning of the study of fractional differential equations involving p-Laplacian under resonant conditions, some researchers have obtained the existence of solutions. However, the proof procedures are wrong. By some mathematical techniques such as pointwise equicontinuity, we give the correct proof.