EMIS ELibM Electronic Journals Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques naturelles / sciences mathematiques
Vol. CXXXIX, No. 34, pp. 75–88 (2009)

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Weak solutions to differential equations with left and right fractional derivatives defined on ${\Bbb R}$

T. M. Atanackovic, S. Pilipovic and B. Stankovic

Faculty of Technical Sciences, Department of Mechanics, University of Novi Sad, 21000 Novi Sad, Serbia
Faculty of Sciences, Department of Mathematics and Informatics, University of Novi Sad, 21000 Novi Sad, Serbia

Abstract: We treat linear differential equations containing both left and right Riemann-Liouville fractional derivatives arising from fractional variational problems. We use the Fourier transform method to obtain weak solution to the problem. Regularity of such solution is examined and the conditions for the existence of classical solution are stated.

Keywords: Right and left Riemann-Liouville fractional derivative; Fractional differential equations. Fourier transform

Classification (MSC2000): 05C50

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Electronic fulltext finalized on: 15 Sep 2009. This page was last modified: 20 Jun 2011.

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