Nonlinear Fuzzy Volterra Integro-differential Equation of N-th Order: Analytic Solution and Existence and Uniqueness of Solution

This paper focuses on the fuzzy Volterra integro-differential equation of nth order of the second-kind with nonlinear fuzzy kernel and initial values. The derived integral equations are solvable, the solutions of which are unique under certain conditions. The existence and uniqueness of the solutions are investigated in a theorem and an upper boundary is found for solutions. Comparison of the exact and approximated solutions shows the least error.

Keywords:

General n−th order derivative , H-derivative , H-difference , Fuzzy n-th Order Integro-differential Equation , Existence and Uniqueness theorem