We firstly present a generalized concept of higher-order differentiability for fuzzy functions. Then we interpret Nth-order fuzzy differential equations using this concept. We introduce new definitions of solution to fuzzy differential equations. Some examples are provided for which both the new solutions and the former ones to the fuzzy initial value problems are presented and compared. We pre...

In this paper we propose Runge-Kutta Fehlberg method for solving fully fuzzy differential equations (FFDEs) of the form y ′ (t) = a⊗ y(t), y(0) = y0, t ∈ [0,T ] under strongly generalized H-differentiability. The algorithm used here is based on cross product of two fuzzy numbers. Using cross product we investigate the problem of finding a numerical approximation of solutions. The convergence of...

In this paper we develop with considerable details a theory of multivector functions of a p-vector variable. The concepts of limit, continuity and differentiability are rigorously studied. Several important types of derivatives for these multivector functions are introduced, as e.g., the A-directional derivative (where A is a p-vector) and the generalized concepts of curl, divergence and gradie...

Hydraulic differential electric servo cylinders are electromechanical tools applicable for driving e.g. manipulators. Actual models are strongly nonlinear, coupled systems of differential equations. In the present paper we propose a new model using fuzzy differential equations under strongly generalized differentiability concept. The key point is a continuous fuzzyfication of the signum functio...

The main purpose of this study is to introduce a new double fuzzy transform called the Sawi transform. A proof some basic properties single and are provided. These results implemented obtain exact solution non-homogeneous linear telegraph equation under generalized Hukuhara partial differentiability. In addition, by using symmetric triangular numbers, numerical examples given demonstrate validi...

In this paper a new method for solving fuzzy differential equation with fractional order is considered. The fuzzy solution is construct by power series in the Caputo derivatives sense. To illustrate the reliability of method some examples are provided. In this paper a new method for solving fuzzy differential equation with fractional order is considered. The fuzzy solution is construct by power...