Project Euclid - mathematics and statistics online

In this paper, we introduce a novel Mittag–Leffler-type function and study its properties in relation to some integro-differential operators involving Hadamard fractional derivatives or hyper-Bessel-type operators. We discuss then the utility of these results to solve some integro-differential equations involving these operators by means of operational methods. We show the advantage of our approach through some examples. Among these, an application to a modified Lamb–Bateman integral equation is presented.