### 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.

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.

#### Keywords

Hadamard type fractional integral equations; measure of noncompactness; existence; uniform local attractivity; local stability

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