In this paper, some properties of pseudo-differential operators, SG-elliptic partial differential equations with polynomial coefficients and localization operators on space S ν (R), are studied by using fractional Fourier transform. AMS Mathematics Subject Classification (2010): 35S05, 46F12, 47G30.

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, 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...

In this paper, we study the Ulam-Hyers-Mittag-Leffler stability for a linear fractional order differential equation with Caputo-type derivative using Fourier transform. Finally, provide an enumeration of chemical reactions equation.

Abstract: Motivated by statistical mechanics contexts, we study the properties of the q-Laplace transform, which is an extension of the well-known Laplace transform. In many circumstances, the kernel function to evaluate certain integral forms has been studied. In this article, we establish relationships between q-exponential and other well-known functional forms, such as Mittag–Leffler functio...

In this article, we survey the asymptotic stability analysis of fractional differential systems with the Prabhakar fractional derivatives. We present the stability regions for these types of fractional differential systems. A brief comparison with the stability aspects of fractional differential systems in the sense of Riemann-Liouville fractional derivatives is also given. 

the aim of this work is to describe the qualitative behavior of the solution set of a givensystem of fractional differential equations and limiting behavior of the dynamical system or flow defined by the system of fractional differential equations. in order to achieve this goal, it is first necessary to develop the local theory for fractional nonlinear systems. this is done by the extension of ...

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...

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...