Pseudo-processes governed by higher-order fractional differential equations.
Beghin, Luisa (2008)
Electronic Journal of Probability [electronic only]
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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...
Abdennadher, Ali, Neel, Marie-Christine (2007)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Luchko, Yury, Mainardi, Francesco, Rogosin, Sergei (2011)
Fractional Calculus and Applied Analysis
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MSC 2010: 26A33 Dedicated to Professor Rudolf Gorenflo on the occasion of his 80th anniversary This paper presents a brief overview of the life story and professional career of Prof. R. Gorenflo - a well-known mathematician, an expert in the field of Differential and Integral Equations, Numerical Mathematics, Fractional Calculus and Applied Analysis, an interesting conversational partner, an experienced colleague, and a real friend. Especially his role in the modern Fractional...
Anh, V. V., McVinish, R. (2003)
Journal of Applied Mathematics and Stochastic Analysis
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Luchko, Yury (2011)
Fractional Calculus and Applied Analysis
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MSC 2010: 26A33, 33E12, 35B45, 35B50, 35K99, 45K05 Dedicated to Professor Rudolf Gorenflo on the occasion of his 80th anniversary In the paper, maximum principle for the generalized time-fractional diffusion equations including the multi-term diffusion equation and the diffusion equation of distributed order is formulated and discussed. In these equations, the time-fractional derivative is defined in the Caputo sense. In contrast to the Riemann-Liouville fractional derivative,...
Li, Ming (2010)
Mathematical Problems in Engineering
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Vázquez, Luis (2011)
Advances in Difference Equations [electronic only]
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Pagnini, Gianni (2011)
Fractional Calculus and Applied Analysis
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MSC 2010: 34A08 (main), 34G20, 80A25 The application of Fractional Calculus in combustion science to model the evolution in time of the radius of an isolated premixed flame ball is highlighted. Literature equations for premixed flame ball radius are rederived by a new method that strongly simplifies previous ones. These equations are nonlinear time-fractional differential equations of order 1/2 with a Gaussian underlying diffusion process. Extending the analysis to self-similar...