We are interested in proposing the convex fuzzy functions from R into E to describe the concepts of left and right Generalized derivatives. In this way, several properties of the concepts are discussed. As well, the notions of Generalized subdifferential for these functions are studied and calculated. Finally, the properties of the concepts are illustrated and applied through some examples.

In the seventy decade the Black Scholes model had a critical role in the pricing of financial derivatives. But later, due to its major weakness, other various models were presented. The class of Levy processes is one of the most common models used for pricing financial assets. The one of this processes is Generalized hyperbolic process that is based on the Generalized hyperbolic distribution.First, In this paper we introduce this distribution and then fit data related to the stock price in Iran market. (Iranian asset returns)

Fuzzy optimization issues have been discussed by many authors in recent articles, inspired by the concepts of Generalized Hukuhara difference and Generalized Hukuhara differentiability for one-dimensional functions from R to E, and have made considerable progress. In this paper, the concept of total Generalized differentiability is introduced by using the concept of Generalized difference from R^n to E for multi-dimensional mappings. Furthermore, the total Generalized differentiability of the above is also examined and then the concept of directional Generalized differentiability and partial Generalized differentiability for fuzzy multi-dimensional mappings is defined and discussed in detail. In addition, directional Generalized differentiability and partial Generalized differentiability are expressed in terms of level-wise Generalized differentiability. Also, the properties and the relationship between them are discussed. Finally, the relationships between total Generalized differentiability, directional Generalized differentiability and partial Generalized differentiability are shown to illustrate the power and ability of relationships between them by mentioning some examples.

The unsmooth boundary will greatly affect motion morphology of a shallow water wave, and a fractal space is introduced to establish a Generalized KdV-Burgers equation with fractal derivatives. The semiinverse method is used to establish a fractal variational formulation of the problem, which provides conservation laws in an energy form in the fractal space and possible solution structures of the equation.

In this research, in order to investigate the effect of the piezoelectric patch which is used as a sensor or actuator in rotating flexible structures such as a helicopter blade, the free vibrations of the rotating rectangular sheet with and without the piezoelectric patch have been presented. First-order shear deformation theory is considered for plate displacement and piezoelectric field. Considering the effect of Coriolis acceleration, centrifugal acceleration and centrifugal in-plane forces, the equations of motion are derived from Hamilton's principle and the electromechanical couple equation is obtained from Maxwell's equation. For piezoelectric, two electrical conditions, open circuit and closed circuit, which are used in sensors and actuators, respectively, have been considered. The equations are discretized with the help of the numerical method of Generalized differential squares and the matrices of inertia mass, eccentricity, Coriolis and stiffness matrix are obtained. Natural frequency values for beam and rotating plate have been compared in Abaqus software. Also, the values obtained from the numerical solution in MATLAB have been verified with articles and ABAQUS, which have high accuracy. The effect of parameters such as hub radius, rotation speed, sheet thickness, aspect ratio, piezoelectric patch thickness and applied voltage on the natural frequency of the system has also been investigated.

The present work treats with a novel Generalized model of higher order derivatives heat conduction. Using Taylor series expansion, the Fourier law of heat conduction is advanced by introducing different phase lags for the heat flux and the temperature gradient vectors. Based on this new model, the thermoelastic behavior of a rotating hollow cylinder is analyzed analytically. The governing differential equations are solved in a numerical form using the Laplace transform technique. Numerical calculations are displayed tables and graphs to clarify the effects of the higher order and the rotation parameters. Finally, the results obtained are verified with those in previous literature.

We present a new and simple direct approach based on Generalized moving least squares (GMLS) for computing the first derivatives of the functions defined on the sphere. The novel method utilizes a Householder transformation (reflection) and a projection onto the tangent plane to compute the first derivatives at the original point on the sphere. The main benefit of this algorithm is that there is no need to use the spherical harmonics for constructing the approximation of the first derivatives. An example of the approximation has been tested to show the ability of the developed method. Moreover, this method has been applied to solve the transport equation in one example.