In this paper, operational matrices of Riemann-Liouville fractional integration and Caputo fractional differentiation for shifted Jacobi polynomials are considered. Using the given initial conditions, we transform the fractional differential equation (FDE) into a modified fractional differential equation with zero initial conditions. Next, all the existing functions in modified differential equ...

So far, many methods have been presented to solve the rst-order di erential equations. But, not many studies have been conducted for numerical solution of high-order fuzzy di erential equations. In this research, First, the equation by reducing time, we transform the rst-order equation. Then we have applied Adams-Bashforth multi-step methods for the initial approximation of one order di erentia...

In this paper we show the existence and uniqueness of fuzzy solutions of the equation du(t)=dt = f(t; u(t)); u(0) = u0 ∈ E, using the properties of Hasegawa’s functionals and successive approximation. c © 2000 Published by Elsevier Science B.V. All rights reserved.

Visual motion distorts the perceived position of a stimulus. In the flash-drag effect (FDE), the perceived position of a flash appears to be shifted in the direction of nearby motion. In the flash-lag effect (FLE), a flash adjacent to a moving stimulus appears to lag behind. The FLE has been explained by several models, including the differential latency hypothesis, that a moving stimulus has a...

We study conditions under which the solutions of a fuzzy integral equation are bounded. 1. Introduction. The concept of set-valued functions and their calculus [2] were found useful in some problems in economics [3], as well as in control theory [17]. Later on, the notion of H-differentiability was introduced by Puri and Ralesku in order to extend the differential of set-valued functions to tha...

In this paper we study numerical methods for hybrid fuzzy fractional differential equation, Degree of Sub element hood and the iteration method is used to solve the hybrid fuzzy fractional differential equations with a fuzzy initial condition.

In this paper the solution of a second order linear differential equations with intuitionistic fuzzy boundary value is described. It is discussed for two different cases: coefficient is positive crisp number and coefficient is negative crisp number. Here fuzzy numbers are taken as generalized trapezoidal intutionistic fuzzy numbers (GTrIFNs). Further a numerical example is illustrated.

Mathematical models in science and engineering often contain parameters that are uncertain. These parameters are usually represented by random numbers, fields or processes. However, when the stochastic characteristics of these parameters are not precisely known, an interval representation, or, more generally, a fuzzy representation may be more appropriate. This leads to so-called fuzzy differen...