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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 |
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Vol. 12 (2017), No. 1, 3–21
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Abstract |
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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. |
Keywords
fractional Sturm–Liouville problem, fractional calculus of
variations, discrete fractional calculus, continuous
fractional calculus
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Milestones
Received: 30 January 2016
Revised: 29 March 2016
Accepted: 4 April 2016
Published: 26 November 2016
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Authors |
| Ricardo Almeida | |
| Center for Research and Development
in Mathematics and Applications Department of Mathematics University of Aveiro 3810-193 Aveiro Portugal |
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| Agnieszka B. Malinowska | |
| Faculty of Computer Science Bialystok University of Technology 15-351 Bialystok Poland |
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| M. Luísa Morgado | |
| Centro de Matemática, pólo
CMAT-UTAD Department of Mathematics University of Trás-os-Montes e Alto Douro 5000-801 Vila Real Portugal |
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| Tatiana Odzijewicz | |
| Department of Mathematics and
Mathematical Economics Warsaw School of Economics 02-554 Warsaw Poland |
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