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Fractional Calculus and Applied Analysis

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Volume 14, Issue 4

Issues

On the existence and uniqueness and formula for the solution of R-L fractional cauchy problem in ℝn

Dariusz Idczak / Rafal Kamocki
Published Online: 2011-09-29 | DOI: https://doi.org/10.2478/s13540-011-0033-5

Abstract

In this paper we obtain results on the existence and uniqueness of a solution to a fractional nonlinear Cauchy problem containing the Riemann-Liouville derivative, in a fractional counterpart of the set of ℝn-valued absolutely continuous functions. We also derive a Cauchy formula for the solution to the linear problem of such a type.

MSC: Primary 34A08, 26A33

Keywords: Riemann-Liouville derivative; fractional Cauchy problem; existence and uniqueness of a solution; Cauchy formula

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About the article

Published Online: 2011-09-29

Published in Print: 2011-12-01


Citation Information: Fractional Calculus and Applied Analysis, Volume 14, Issue 4, Pages 538–553, ISSN (Online) 1314-2224, ISSN (Print) 1311-0454, DOI: https://doi.org/10.2478/s13540-011-0033-5.

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© 2011 Diogenes Co., Sofia. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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