On Some Operators Involving Hadamard Derivatives

Abstract

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.

References in corpus (2)

• Analytic solutions of fractional differential equations by operational methods
• Integral equations, fractional calculus and shift operator

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