Solving the homogeneous BVP of second order linear FDEs with fuzzy parameters under granular differentiability concept1

Abstract

In this paper, the second-order fuzzy homogeneous differential equation is transformed into a more special simplest form under the condition that the solution of the boundary value problem of the equation exists and is unique. Then the eigenvalues of the boundary value problem of the second-order simplest fuzzy homogeneous differential equation are studied and the theorems that make the eigenvalues exist are proposed and then illustrated with examples. Finally, it is proved that when the second-order fuzzy coefficient p ˜ ( t ) in the second-order fuzzy homogeneous differential equation is a fuzzy number, the solution set of its corresponding second-order granular homogeneous differential equation becomes larger, that is, the solution set of fuzzy differential equations with real numbers is a subset of the solution set with fuzzy coefficients as fuzzy numbers.