The present paper deals with the study of a generalized Mittag-Leffler function and associated fractional operator. The operator has been discussed in the space of Lebesgue measurable functions. The composition with Riemann–Liouville fractional integration operator has been obtained.

A Reply to the Comment by M. W. Matsen.

UDC 517.5 The paper deals with solving the integral equation with a generalized Mittag-Leffler function $E_{\alpha ,\beta }^{\gamma ,q}(z)$ that defines a kernel using a fractional integral operator. The existence of the solution is justified and necessary conditions on the integral equation admiting a solution are discussed. Also, the solution of the integral equation is derived.