Chaos Expansion Methods for Stochastic Differential Equations Involving the Malliavin Derivative–Part I
Tijana Levajković, Dora Seleši (2011)
Publications de l'Institut Mathématique
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Tijana Levajković, Dora Seleši (2011)
Publications de l'Institut Mathématique
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Salah Hajji (2008)
Annales mathématiques Blaise Pascal
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We study a stochastic fractional partial differential equations of order driven by a compensated Poisson measure. We prove existence and uniqueness of the solution and we study the regularity of its trajectories.
Rajkovic, Predrag, Marinkovic, Sladjana, Stankovic, Miomir (2007)
Fractional Calculus and Applied Analysis
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Mathematics Subject Classification: 33D60, 33E12, 26A33 Based on the fractional q–integral with the parametric lower limit of integration, we consider the fractional q–derivative of Caputo type. Especially, its applications to q-exponential functions allow us to introduce q–analogues of the Mittag–Leffler function. Vice versa, those functions can be used for defining generalized operators in fractional q–calculus.
Kilbas, Anatoly (2005)
Fractional Calculus and Applied Analysis
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Mathematics Subject Classification: 26A33, 33C20. The paper is devoted to the study of the fractional calculus of the generalized Wright function pΨq(z) defined for z ∈ C, complex ai, bj ∈ C and real αi, βj ∈ R (i = 1, 2, · · · p; j = 1, 2, · · · , q) by the series pΨq (z) It is proved that the Riemann-Liouville fractional integrals and derivative of the Wright function are also the Wright functions but of greater order. Special cases are considered. * The present...
Atanackovic, T., Stankovic, B. (2004)
Fractional Calculus and Applied Analysis
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An expansion formula for fractional derivatives given as in form of a series involving function and moments of its k-th derivative is derived. The convergence of the series is proved and an estimate of the reminder is given. The form of the fractional derivative given here is especially suitable in deriving restrictions, in a form of internal variable theory, following from the second law of thermodynamics, when applied to linear viscoelasticity of fractional derivative type. ...
Saxena, R. K., Saigo, Megumi (2005)
Fractional Calculus and Applied Analysis
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Mathematics Subject Classification: 26A33, 33E12, 33C20. It has been shown that the fractional integration and differentiation operators transform such functions with power multipliers into the functions of the same form. Some of the results given earlier by Kilbas and Saigo follow as special cases.
Takači, Dj., Takači, A. (2010)
Fractional Calculus and Applied Analysis
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MSC 2010: 26A33, 44A45, 44A40, 65J10 We consider a linear system of differential equations with fractional derivatives, and its corresponding system in the field of Mikusiński operators, written in a matrix form, by using the connection between the fractional and the Mikusiński calculus. The exact and the approximate operational solution of the corresponding matrix equations, with operator entries are determined, and their characters are analyzed. By using the packages...
El-Borai, Mahmoud M. (2004)
Boletín de la Asociación Matemática Venezolana
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Sharma, Manoj (2008)
Fractional Calculus and Applied Analysis
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Mathematics Subject Classification: 26A33, 33C60, 44A15 In this paper a new special function called as M-series is introduced. This series is a particular case of the H-function of Inayat-Hussain. The M-series is interesting because the pFq -hypergeometric function and the Mittag-Leffler function follow as its particular cases, and these functions have recently found essential applications in solving problems in physics, biology, engineering and applied sciences. Let us note...
Purohit, S.D., Raina, R.K. (2009)
Acta Mathematica Universitatis Comenianae. New Series
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