In the traditional approach to differentiability, found in almost all university textbooks, this notion is considered only for interior points of domain function or functions with an open domain. This leads fact that differentiability has usually been Rn, which severely limits possibility applying potential techniques and tools differential calculus a broader class functions. Although there gre...

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in this paper a numerical method for solving forth order fuzzy dierentialequations under generalized differentiability is proposed. this method is basedon the interpolating a solution by piecewise polynomial of degree 8 in the rangeof solution . we investigate the existence and uniqueness of solutions. finally anumerical example is presented to illustrate the accuracy of the new technique.

In this paper, we consider two new uniqueness results for fuzzy fractional differential equations (FFDEs) involving Riemann-Liouville generalized H-differentiability with the Nagumo-type condition and the Krasnoselskii-Krein-type condition. To this purpose, the equivalent integral forms of FFDEs are determined and then these are used to study the convergence of the Picard successive approximati...

In this paper, Picard method is proposed to solve the Cauchy reaction-diffusion equation with fuzzy initial condition under generalized H-differentiability. The existence and uniqueness of the solution and convergence of the proposed method are proved in details. Some examples are investigated to verify convergence results and to illustrate the efficiently of the method. Also, we obtain the swi...

We study analyticity, differentiability, and semismoothness of Löwner’s operator and spectral functions under the framework of Euclidean Jordan algebras. In particular, we show that many optimization-related classical results in the symmetric matrix space can be generalized within this framework. For example, the metric projection operator over any symmetric cone defined in a Euclidean Jordan a...

In this paper, we study linear fuzzy time-variant optimal control systems using the generalized differentiability concept and we present the general form of optimal controls and states. Some examples are provided to illustrate our results.

In this paper, the solution to Fuzzy sequential Fractional Initial Value Problem [FFIVP] under Caputo type fuzzy fractional derivatives by a modified fractional Euler method is presented. The Caputo-type fuzzy fractional derivatives are defined based on Hukuhara difference and strongly generalized fuzzy differentiability. The modified fractional Euler method based on a generalized Taylors formu...

In this paper, We interpret a fuzzy differential equation by using the strongly generalized differentiability concept. Utilizing the Generalized characterization Theorem. Then a novel hybrid method based on learning algorithm of fuzzy neural network for the solution of differential equation with fuzzy initial value is presented. Here neural network is considered as a part of large field called ...