Mathematics and Statistics Vol. 12(5), pp. 494 - 500
DOI: 10.13189/ms.2024.120511
Reprint (PDF) (305Kb)

Solutions of Fuzzy Fractional Boundary Value Problems: A Novel Approach

V. Padmapriya ^1,2, M. Kaliyappan ^1,*
1 Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai, India
² New Prince Shri Bhavani Arts and Science College, Chennai, India

ABSTRACT

In this paper, the solution of fractional boundary value problem with fuzzy boundary conditions is investigated. The fuzzy fractional boundary value problem is decomposed into collections of classical fractional boundary value problems. Then Adomian decomposition method is applied to solve these classical fractional boundary value problems. The collection of all solutions to these fractional boundary value problems provide the solution to the fuzzy fractional boundary value problem. The solution to this problem is expressed in terms of a fuzzy collection of crisp real functions. The boundary value problem is satisfied by every real function in the solution set. The degree of membership of each function is determined by the minimum membership degree among its associated fuzzy boundary values. It can be demonstrated that if the corresponding fractional problem has a unique solution, then the fuzzy fractional problem also has one. It showed that when triangular fuzzy numbers are assigned to the boundary values, the resulting solution at a specific time also takes the form of a triangular fuzzy number. An example is provided to explain the suggested method.

KEYWORDS
Fuzzy Set, Fuzzy Fractional Boundary Value Problem, Fuzzy Fractional Differential Equations, Adomian Decomposition Method

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] V. Padmapriya , M. Kaliyappan , "Solutions of Fuzzy Fractional Boundary Value Problems: A Novel Approach," Mathematics and Statistics, Vol. 12, No. 5, pp. 494 - 500, 2024. DOI: 10.13189/ms.2024.120511.

(b). APA Format:
V. Padmapriya , M. Kaliyappan (2024). Solutions of Fuzzy Fractional Boundary Value Problems: A Novel Approach. Mathematics and Statistics, 12(5), 494 - 500. DOI: 10.13189/ms.2024.120511.