In this manuscript, the proposed work is to study the existence of second-order differential equations with three point boundary conditions. Existence is proved using fuzzy set valued mappings of a real variable whose values are normal, convex, upper semi continuous and compactly supported fuzzy sets. The sufficient conditions are also provided to establish the existence results of fuzzy solutions of second order differential equations for three point boundary value problem. By using Banach fixed point principle, a new existence theorem of solutions for these equations in the metric space of normal fuzzy convex sets with distance given by the maximum of the Hausdorff distance between level sets is obtained. Then to further establish the existence, fixed point theorem for absolute retracts is used by taking consideration that space of fuzzy sets can be embedded isometrically as a cone in Banach space. Finally, an example is provided to illustrate the result.
Chalishajar, Dimplekumar N. and Ramesh, R.
Fuzzy Solutions to Second Order Three Point Boundary Value Problem,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 15,
2, Article 11.
Available at: https://digitalcommons.pvamu.edu/aam/vol15/iss2/11