Exact solution for the fractional cable equation with nonlocal boundary conditions

• Authors: Emilia Bazhlekova , Ivan Dimovski
• Languages of publication: EN

Abstracts

EN

The fractional cable equation is studied on a bounded space domain. One of the prescribed boundary conditions is of Dirichlet type, the other is of a general form, which includes the case of nonlocal boundary conditions. In real problems nonlocal boundary conditions are prescribed when the data on the boundary can not be measured directly. We apply spectral projection operators to convert the problem to a system of integral equations in any generalized eigenspace. In this way we prove uniqueness of the solution and give an algorithm for constructing the solution in the form of an expansion in terms of the generalized eigenfunctions and three-parameter Mittag-Leffler functions. Explicit representation of the solution is given for the case of double eigenvalues. We consider some examples and as a particular case we recover a recent result. The asymptotic behavior of the solution is also studied.

Keywords

EN

cable equation; anomalous diffusion; fractional derivative; three-parameter Mittag-Leffler function

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2013
• Volume: 11
• Issue: 10
• Pages: 1304-1313

Dates

published

1 - 10 - 2013

online

19 - 12 - 2013

Contributors

author

Emilia Bazhlekova

• Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 8, Sofia, 1113, Bulgaria

author

Ivan Dimovski

• Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 8, Sofia, 1113, Bulgaria

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Identifiers

DOI

10.2478/s11534-013-0213-5