Usage of fuzzy differential equations (FDEs) is a natural way to model dynamical systems under possibilistic uncertainty. We consider second order hybrid fuzzy differentia

In this paper, a Bernoulli pseudo-spectral method for solving nonlinear fractional Volterra integro-differential equations is considered. First existence of a unique solution for the problem under study is proved. Then the Caputo fractional derivative and Riemman-Liouville fractional integral properties are employed to derive the new approximate formula for unknown function of the problem....

The design of the optimal fuzzy fractional-order PID controller is addressed in this work. A multi-objective genetic algorithm is proposed to design rule base and membership functions of the fuzzy logic systems. Three conflicting objective functions in both time and frequency domains have been used in Pareto design of the fuzzy fractional-order PID controller. The simulation results reveal the ...

in this article, we develop the distributed order fractional hybrid differential equations (dofhdes) with linear perturbations involving the fractional riemann-liouville derivative of order $0 < q < 1$ with respect to a nonnegative density function. furthermore, an existence theorem for the fractional hybrid differential equations of distributed order is proved under the mixed $varphi$-lipschit...

In this paper we introduce some stability criteria for impulsive fuzzy system of differential equations with finite delay in states. Firstly, a new comparison principle for fuzzy differential system compared to crisp ordinary differential equation, based on a notion of upper quasi-monotone nondecreasing, in N dimentional state space is presented. Furthermore, in order to analyze the stability o...

‎It is commonly accepted that fractional differential equations play‎ ‎an important role in the explanation of many physical phenomena‎. ‎For‎ ‎this reason we need a reliable and efficient technique for the‎ ‎solution of fractional differential equations‎. ‎This paper deals with‎ ‎the numerical solution of a class of fractional differential‎ ‎equation‎. ‎The fractional derivatives are described...

in recent years, there has been greater attempt to find numerical solutions of differential equations using wavelet&apos;s methods. the following method is based on vector forms of haar-wavelet functions. in this paper, we will introduce one dimensional haar-wavelet functions and the haar-wavelet operational matrices of the fractional order integration. also the haar-wavelet operational matrice...

In this paper the exact and the approximate solutions of fuzzy fractional differential equation, in the sense of Caputo Hukuhara differentiability, with a fuzzy condition are constructed by using the fuzzy Laplace transform. The obtained solutions are expressed in the form of the fuzzy Mittag-Leffler function. The presented procedure is visualized and the graphs of the obtained approximate solu...

approximating the solution of differential equations of fractional order is necessary because fractional differential equations have extensively been used in physics, chemistry as well as engineering fields. in this paper with central difference approximation and newton cots integration formula, we have found approximate solution for a class of boundary value problems of fractional order. three...

In this paper, we study semi-analytical methods entitled Homotopy pertourbation method (HPM) to solve fuzzy impulsive fractional differential equations based on the concept of generalized Hukuhara differentiability. At the end first of Homotopy pertourbation method is defined and its properties are considered completely. Then econvergence theorem for the solution are proved and we will show tha...