Study on a quadratic Hadamard type fractional integral equation on an unbounded interval

Abstract

In this paper, a quadratic Hadamard type fractional integral equations on an unbounded interval is studied. By applying a technique of measure of noncompactness and Schauder fixed point theorem, existence and uniform local attractivity of solutions are presented after overcoming some difficulty from the Hadamard type singular kernel. Moreover, three new solutions sets who tend to zero at infinity are constructed to obtain local stability of solutions. Finally, two examples are made to illustrate our theory results.