Vol. 12, No. 1, 2017

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Variational methods for the solution of fractional discrete/continuous Sturm–Liouville problems

Ricardo Almeida, Agnieszka B. Malinowska, M. Luísa Morgado and Tatiana Odzijewicz

Vol. 12 (2017), No. 1, 3–21

The fractional Sturm–Liouville eigenvalue problem appears in many situations, e.g., while solving anomalous diffusion equations coming from physical and engineering applications. Therefore, obtaining solutions or approximations of solutions to this problem is of great importance. Here, we describe how the fractional Sturm–Liouville eigenvalue problem can be formulated as a constrained fractional variational principle and show how such formulation can be used in order to approximate the solutions. Numerical examples are given to illustrate the method.

fractional Sturm–Liouville problem, fractional calculus of variations, discrete fractional calculus, continuous fractional calculus
Received: 30 January 2016
Revised: 29 March 2016
Accepted: 4 April 2016
Published: 26 November 2016
Ricardo Almeida
Center for Research and Development in Mathematics and Applications
Department of Mathematics
University of Aveiro
3810-193 Aveiro
Agnieszka B. Malinowska
Faculty of Computer Science
Bialystok University of Technology
15-351 Bialystok
M. Luísa Morgado
Centro de Matemática, pólo CMAT-UTAD
Department of Mathematics
University of Trás-os-Montes e Alto Douro
5000-801 Vila Real
Tatiana Odzijewicz
Department of Mathematics and Mathematical Economics
Warsaw School of Economics
02-554 Warsaw