A method for second-order linear fuzzy two-point boundary value problems based on the Hukuhara differentiability

Document Type : Research Paper


Department of Mathematics, Arak Branch, Islamic Azad University, Arak, Iran.


In this paper, we deal with second-order fuzzy linear two-point boundary value problems (BVP) under Hukuhara derivatives. Considering the first-order and second-order Hukuhara derivatives, four types of fuzzy linear two-point BVPs can be obtained where each may or may not have a solution. Therefore a fuzzy two-point (BVP) may have one, two, three, or four different kinds of solutions concerning this kind of derivative. To solve this fuzzy linear two-point (BVP), we convert each to two cases of crisp boundary value problems. We apply a standard method(numerical or analytical) to solve crisp two-point BVPs in their domain. Subsequently, the crisp solutions are combined to obtain a fuzzy solution to the fuzzy problems, and the solutions are checked to see if they satisfy the fuzzy issues. Conditions are presented under which fuzzy problems have the fuzzy solution and illustrated with some examples.


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