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Stochastic Solution of a KPP-Type Nonlinear Fractional Differential Equation

Cipriano, F.; Ouerdiane, H.; Vilela Mendes, R. — 2009

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 26A33, 76M35, 82B31 A stochastic solution is constructed for a fractional generalization of the KPP (Kolmogorov, Petrovskii, Piskunov) equation. The solution uses a fractional generalization of the branching exponential process and propagation processes which are spectral integrals of Levy processes.

Generalized Fractional Evolution Equation

Da Silva, J. L.; Erraoui, M.; Ouerdiane, H. — 2007

Fractional Calculus and Applied Analysis

2000 Mathematics Subject Classification: Primary 46F25, 26A33; Secondary: 46G20 In this paper we study the generalized Riemann-Liouville (resp. Caputo) time fractional evolution equation in infinite dimensions. We show that the explicit solution is given as the convolution between the initial condition and a generalized function related to the Mittag-Leffler function. The fundamental solution corresponding to the Riemann-Liouville time fractional evolution equation does not admit a...

Distributions gaussiennes et temps locaux d'intersection

H. Ouerdiane; A. Rezgui — 2000

Revista Matemática Complutense

Quantum Lévy-type Laplacian and associated stochastic differential equations

A. Barhoumi; H. Ouerdiane — 2006

Banach Center Publications

We study a quantum extension of the Lévy Laplacian, so-called quantum Lévy-type Laplacian, to the nuclear algebra of operators on spaces of entire functions. We give several examples of the action of the quantum Lévy-type Laplacian on basic operators and we study a quantum white noise convolution differential equation involving the quantum Lévy-type Laplacian.

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