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Applications of the fractional Sturm-Liouville problem to the space-time fractional diffusion in a finite domain

  • Małgorzata Klimek EMAIL logo , Agnieszka B. Malinowska EMAIL logo and Tatiana Odzijewicz EMAIL logo
Published/Copyright: May 4, 2016

Abstract

The space–time fractional diffusion equations on finite domain model anomalous diffusion behavior with large particle jumps combined with long waiting times. In this work we prove existence of strong solutions for such equations. Our proofs strongly depend on the fractional Sturm–Liouville theory, precisely on the problem of finding eigenvalues and corresponding eigenfunctions to the certain fractional differential equation. Using the method of separating variables and applying theorem ensuring existence of solutions to the fractional Sturm–Liouville problem we solve several types of fractional diffusion equations.

MSC 2010: 26A33; 49R02; 47A75

Please cite to this paper as published in: Fract. Calc. Appl. Anal., Vol. 19, No 2 (2016), pp. 516–550, DOI: 10.1515/fca-2016-0027


Acknowledgement

Research supported under Czestochowa University of Technology project BS/PB-1-105-3010/2011/S (M. Klimek), Bialystok University of Technology grant S/WI/1/16 (A.B. Malinowska) and by the Warsaw School of Economics grant KAE/S15/35/15 (T. Odzijewicz). The authors are grateful to Jacky Cresson for fruitful discussions during the Joint Meeting of the German Mathematical Society (DMV) and the Polish Mathematical Society (PTM), 17–20 September 2014, Pozna ǹ, Poland.

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Received: 2015-6-1
Revised: 2016-2-8
Published Online: 2016-5-4
Published in Print: 2016-4-1

© 2016 Diogenes Co., Sofia

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