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Conditions for the existence of a classical solution of a cauchy type problem for the diffusion equation with a Riemann-Liouville partial derivative

Conditions for the existence of a classical solution of a cauchy type problem for the diffusion... We study a Cauchy type problem for a differential equation containing a fractional Riemann-Liouville partial derivative of order α, 0 < α < 2. Conditions under which the solution of the problem tends to zero as |x| → ∞ are obtained. We prove an existence theorem for a classical solution of the Cauchy type problem and show that the solution has a singularity as t → 0 of order 1 − α if 0 < α ≤ 1 and of order 2 − α if 1 < α < 2. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Conditions for the existence of a classical solution of a cauchy type problem for the diffusion equation with a Riemann-Liouville partial derivative

Voroshilov, A.; Kilbas, A.
Differential Equations , Volume 44 (6) – Sep 9, 2008
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References (6)

Publisher
Springer Journals
Copyright
Copyright © 2008 by MAIK Nauka
Subject
Mathematics; Difference and Functional Equations; Partial Differential Equations; Ordinary Differential Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1134/S0012266108060050
Publisher site
See Article on Publisher Site

Abstract

We study a Cauchy type problem for a differential equation containing a fractional Riemann-Liouville partial derivative of order α, 0 < α < 2. Conditions under which the solution of the problem tends to zero as |x| → ∞ are obtained. We prove an existence theorem for a classical solution of the Cauchy type problem and show that the solution has a singularity as t → 0 of order 1 − α if 0 < α ≤ 1 and of order 2 − α if 1 < α < 2.

Journal

Differential Equations – Springer Journals

Published: Sep 9, 2008

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