Affiliation:
1. Faculty of Mathematics , Kim Il Sung University , Ryomyong Street, Daesong District , Pyongyang , D.P.R. Korea
Abstract
Abstract
In the present work, we consider the Cauchy problem for the time fractional diffusion equation involving the general Caputo-type differential operator proposed by Kochubei [11]. First, the existence, the positivity and the long time behavior of solutions of the diffusion equation without source term are established by using the Fourier analysis technique. Then, based on the representation of the solution of the inhomogenous linear ordinary differential equation with the general Caputo-type operator, the general diffusion equation with source term is studied.
Subject
Applied Mathematics,Analysis
Reference28 articles.
1. A. Chechkin, I. M. Sokolov, J. Klafter, Natural and modified forms of distributed-order fractional diffusion equations. In: Fractional Dynamics: Recent Advances, World Scientific, Singapore (2014), 107–127.
2. F. Demengel, G. Demengel, Functional Spaces for the Theory of Elliptic Partial Differential Equations. Springer, London (2012).
3. S.D. Eidelman, A.N. Kochubei, Cauchy problem for fractional diffusion equations. J. Differ. Equ. 199 (2004), 211–255.
4. I. Golding, E.C. Cox, Physical nature of bacterial cytoplasm. Phys. Rev. Lett. 96 (2006), # 098102.
5. H. Jiang, F. Liu, I. Turner, K. Burrage, Analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations on a finite domain. J. Math. Anal. Appl. 389 (2012), 1117–1127.
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