The use of fractional calculus in probability
Gomes, M.I., Pestana, D.D. (1978)
Portugaliae mathematica
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Gomes, M.I., Pestana, D.D. (1978)
Portugaliae mathematica
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Beghin, Luisa (2008)
Electronic Journal of Probability [electronic only]
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Mainardi, Francesco, Mura, Antonio, Pagnini, Gianni (2010)
International Journal of Differential Equations
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Mainardi, Francesco, Gorenflo, Rudolf, Vivoli, Alessandro (2005)
Fractional Calculus and Applied Analysis
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2000 MSC: 26A33, 33E12, 33E20, 44A10, 44A35, 60G50, 60J05, 60K05. After sketching the basic principles of renewal theory we discuss the classical Poisson process and offer two other processes, namely the renewal process of Mittag-Leffler type and the renewal process of Wright type, so named by us because special functions of Mittag-Leffler and of Wright type appear in the definition of the relevant waiting times. We compare these three processes with each other, furthermore...
Mathai, A. (2010)
Fractional Calculus and Applied Analysis
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Mathematical Subject Classification 2010:26A33, 33E99, 15A52, 62E15. Mittag-Leffler functions and their generalizations appear in a large variety of problems in different areas. When we move from total differential equations to fractional equations Mittag-Leffler functions come in naturally. Fractional reaction-diffusion problems in physical sciences and general input-output models in other disciplines are some of the examples in this direction. Some basic properties of Mittag-Leffler...
Kiryakova, Virginia (2011)
Union of Bulgarian Mathematicians
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Виржиния С. Кирякова - В този обзор илюстрираме накратко наши приноси към обобщенията на дробното смятане (анализ) като теория на операторите за интегриране и диференциране от произволен (дробен) ред, на класическите специални функции и на интегралните трансформации от лапласов тип. Показано е, че тези три области на анализа са тясно свързани и взаимно индуцират своето възникване и по-нататъшно развитие. За конкретните твърдения, доказателства и примери, вж. Литературата. ...
Samuel, M., Thomas, Anitha (2010)
Fractional Calculus and Applied Analysis
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MSC 2010: 26A33, 33E12, 33C60, 35R11 In this paper we derive an analytic solution for the fractional Helmholtz equation in terms of the Mittag-Leffler function. The solutions to the fractional Poisson and the Laplace equations of the same kind are obtained, again represented by means of the Mittag-Leffler function. In all three cases the solutions are represented also in terms of Fox's H-function.
Kumar, Dilip, Kilbas, Anatoly (2010)
Fractional Calculus and Applied Analysis
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MSC 2010: 44A20, 33C60, 44A10, 26A33, 33C20, 85A99 The fractional calculus of the P-transform or pathway transform which is a generalization of many well known integral transforms is studied. The Mellin and Laplace transforms of a P-transform are obtained. The composition formulae for the various fractional operators such as Saigo operator, Kober operator and Riemann-Liouville fractional integral and differential operators with P-transform are proved. Application of the P-transform...
Debnath, Lokenath (2003)
International Journal of Mathematics and Mathematical Sciences
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Дж. Тукый ([unknown])
Matematiceskij sbornik
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