Two point fuzzy boundary value problem with eigenvalue parameter contained in the boundary condition

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Authors :

Tahir Ceylan 1 * and Nihat Altınısık 2

Author Address :

1 Department of Mathematics, Faculty of Arts and Sciences, Sinop University, 57000, Sinop, Turkey.
2 Department of Mathematics, Faculty of Arts and Sciences, Ondokuz Mayıs University, 55139, Kurupelit, Samsun, Turkey.

*Corresponding author.

Abstract :

In this article two point fuzzy boundary value problem is defined under the approach generalized Hukuhara differentiability (gH-differentiability). We research the solution method of the fuzzy boundary problem with the basic solutions $ widehat{Phi } left( x,lambda ight) $ and $ widehat{chi } left( x,lambda ight) $ which are defined by the special procuder. We give operator-theoretical formulation, construct fundamental solutions and investigate some properties of the eigenvalues and corresponding eigenfunctions of the considered fuzzy problem. Then results of the proposed
method are illustrated with a numerical example.

Keywords :

gH-derivative, eigenvalue, fuzzy eigenfunction, fuzzy Hilbert Space.



Article Info :

Received : August 21, 2018; Accepted : October 26, 2018.



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