On the Solvability of Caputo -Fractional Boundary Value Problem Involving -Laplacian Operator | Zendy

Hüseyin Aktuğlu | Zendy; Mehmet Ali Özarslan | Zendy

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On the Solvability of Caputo -Fractional Boundary Value Problem Involving -Laplacian Operator

Author(s) -

Hüseyin Aktuğlu,

Mehmet Ali Özarslan

Publication year - 2013

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2013/658617

Subject(s) - mathematics , boundary value problem , operator (biology) , laplace operator , contraction principle , fractional calculus , fractional laplacian , mathematical analysis , p laplacian , fixed point theorem , biochemistry , chemistry , repressor , transcription factor , gene

We consider the model of a Caputo -fractional boundary valueproblem involving -Laplacian operator. By using the Banach contractionmapping principle, we prove that, under some conditions, the suggested modelof the Caputo -fractional boundary value problem involving -Laplacianoperator has a unique solution for both cases of and . It isinteresting that in both cases solvability conditions obtained here depend on, , and the order of the Caputo -fractional differential equation. Finally, we illustrate our results with some examples

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