Solvability Of Some Caputo-Hadamard Fractional Differential Equations Boun-Dary Value Problems

In this paper,the solvability of boundary value problems for several classes of Caputo-Hadamard fractional differential equations is studied,and some sufficient conditions for the existence of solutions are obtained.First of all,we use the alternative theorem in the fixed point theorem to study the existence and uniqueness of solutions for boundary value problems of fractional differential equations with Caputo-Hadamard derivatives;Secondly,we study the existence and uniqueness of positive solutions for three-point boundary value problems of singular nonlinear fractional differential equations with Hadamard type derivatives by using the mixed monotone operator method;Finally,we obtain the solvability results of impulsive boundary value problems for higher order Caputo-Hadamard fractional differential equations,and generalize some existing results on the solvability of impulsive Caputo-Hadamard fractional boundary value problems.The results of this paper improve the Caputo-Hadamard type fractional calculus theory and generalize some conclusions on the solvability of boundary value problems of fractional differential equations.