On the Initial-Boundary Problem for the Time-Fractional Diffusion Equation in the Quarter Plane

2013/06/07 by Demian Nahuel Goos, Gabriela Reyero, Goos, Demian +5
Mathematics · #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.1306.1748

openalex publication_date 2013/06/07 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Taking into account the asymptotic behavior of some Wright functions and the existence of bounds for the Mainardi and the Wright function W(-x,\fracα2, 1) in ℝ⁺ , three different initial-boundary-value problems for the time-fractional diffusion equation in the quarter plane, where the time-fractional derivative is taken in the Caputo sense of order α ∈ (0,1) are solved. Moreover, the limit when α\nearrow 1 of the respective solutions are analyzed, recovering the respective solutions of the classical boundary-value problems when α=1 and the fractional diffusion equation becomes the heat equation.

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