On some operators involving Hadamard derivatives

By Roberto Garra, Federico Polito. 2013

80 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/5a2563a40577ea37a4e76b2bef894ef51bb578d1

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In Applied Mathematics

1. Sergei Rogosin
2. Federico Polito
3. Roberto Garra
4. Enzo Orsingher
5. Luisa Beghin
6. M. Mamchuev

In Modeling and Simulation

1. Sergei Rogosin
2. Federico Polito
3. Roberto Garra
4. Enzo Orsingher
5. Luisa Beghin
6. M. Mamchuev

Citations in the corpus

• The Role of the Mittag-Leffler Function in Fractional Modeling (2015, methodology): “(18) Recently, the Le Roy-type function Equation (4), namely the function, has been introduced independently by Gerhold [40] and jointly by Garra and Polito [41].”
• A Note on Hadamard Fractional Differential Equations with Varying Coefficients and Their Applications in Probability (2017, methodology): “In [4], we called this special function α-Mittag–Leffler function, since it includes for α = 1 the well-known two-parameters Mittag–Leffler function”