In this paper, we study the qualitative behavior of the positive solutions of a second-order rational fuzzy difference equations with initial conditions and parameters are positive fuzzy numbers. More precisely, we investigate existence of positive solutions, boundedness, persistence and stability analysis of a second-order fuzzy rational difference equation. Some numerical examples are given to verify our theoretical results.

In the recent past, multi-term fractional equations have been studied using symmetry methods. In some cases, many practical test problems with some symmetries are provided to demonstrate the authenticity and utility of the used techniques. Fractional-order differential equations can be formulated by using two types of differential operators: single-term and multi-term differential operators. Boundary value problems with single- as well as multi-term differential operators have been extensively studied, but several multi-term fractional differential equations still need to be formulated, and examination should be done with symmetry or any other feasible techniques. Therefore, the purpose of the present research work is the formulation and study of a new couple system of multi-term fractional differential equations with delay, as well as supplementation with nonlocal boundary conditions. After model formulation, the existence of a solution and the uniqueness conditions will be developed, utilizing fixed point theory and functional analysis. Moreover, results related to Ulam’s and other types of functional stability will be explored, and an example is carried out to illustrate the findings of the work.