The equivalent system for a multiple-rational-order (MRO) fractional differential system is studied, where the fractional derivative is in the sense of Caputo or Riemann-Liouville. With the relationship between the Caputo derivative and the generalized fractional derivative, we can change the MRO fractional differential system with a Caputo derivative into a higher-dimensional system with the s...

hybrid system is a dynamic system that exhibits both continuous and discrete dynamic behavior‎. ‎the hybrid differential equations have a wide range of applications in science and engineering‎. ‎the hybrid systems are devoted to modeling‎, ‎design‎, ‎and validation of interactive systems of computer programs and continuous systems‎. ‎hybrid fuzzy differential equations (hfdes) is considered by ...

In this paper, solution of fuzzy differential equation under general differentiability is obtained by simulink. The simulink solution is equivalent or very close to the exact solution of the problem. Accuracy of the simulink solution to this problem is qualitatively better. An illustrative numerical example is presented for the proposed method. Keywords—Fuzzy differential equation, Generalized ...

This article studies differentiability properties for a reformulation of a player convex generalized Nash equilibrium problem as a constrained and possibly nonsmooth minimization problem. By using several results from parametric optimization we show that, apart from exceptional cases, all locally minimal points of the reformulation are differentiability points of the objective function. This ju...

This paper is devoted to the study of gH-Clarke derivative for interval-valued functions. To find properties derivative, concepts limit superior, inferior, and sublinear functions are studied in sequel. It proved that upper a gH-Lipschitz continuous function (IVF) always exists. For convex IVF, found be identical with gH-directional derivative. observed IVF. Several numerical examples provided ...

in this paper, a new approach for solving the second order fuzzy differential equations (fde) with fuzzy initial value, under strongly generalized h-differentiability is presented. solving first order fuzzy differential equations by extending 1-cut solution of the original problem and solving fuzzy integro-differential equations has been investigated by some authors (see for example cite{darabi...

In this paper we study a fuzzy predator-prey model with functional response arctan(ax). The derivatives are approximated using the generalized Hukuhara derivative. To execute numerical simulation, use Runge-Kutta method. results obtained over time for evolution and population presented numerically graphically some conclusions.

In this paper a numerical method for solving second order fuzzy differential equations under generalized differentiability is proposed. This method is based on the interpolating a solution by piecewise polynomial of degree 4 in the range of solution. Moreover we investigate the existence, uniqueness and convergence of approximate solutions. Finally the accuracy of piecewise approximate method b...

In this paper we intend to offer new numerical methods to solve the second-order fuzzy Abel-Volterraintegro-differential equations under the generalized $H$-differentiability. The existence and uniqueness of thesolution and convergence of the proposed methods are proved in details and the efficiency of the methods is illustrated through a numerical example.