In this article, we introduce the fractional differential systems in the sense of the Weber fractional derivatives and study the asymptotic stability of these systems. We present the stability regions and then compare the stability regions of fractional differential systems with the Riemann-Liouville and Weber fractional derivatives.

Making use of a differential operator the author investigate the various impartant properties and characteristics of the subclass Tj(n,m, p, q, α) (p, j,m ∈ N = {1, 2, . . .}, q, n ∈ N0 = N ∪ {0}, 0 ≤ α < p − q) of p-valently analytic functions with negative coefficients. Finally, several applications involving an integral operator and certain fractional calculus operators are also considered.

We prove a Liouville-type theorem for bounded stable solutions v ∈ C(R) of elliptic equations of the type (−∆)v = f(v) in R, where s ∈ (0, 1) and f is any nonnegative function. The operator (−∆) stands for the fractional Laplacian, a pseudo-differential operator of symbol |ξ|.

We investigate a boundary value problem for partial differential equation with Cauchy-Euler fractional operator $$\begin{aligned} x^{2\alpha }D_{*,x}^{2\alpha } u(x,y)+ x^{\alpha }D_{*,x}^{\alpha u(x,y) + u_{yy}(x,y)=f(x,y),\ 0< x<\infty ,\ 0<y< 1,\ 0<\alpha < 1. \end{aligned}$$ The limitations on convergence of series and the Mellin transform lead to search solutions in class functions, which ...

The aim of this work is to describe the qualitative behavior of the solution set of a given system 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...

‎In this article‎, ‎the multi-step conformable fractional differential transform method (MSCDTM) is applied to give approximate solutions of the conformable fractional-order differential systems‎. ‎Moreover‎, ‎we check the stability of conformable fractional-order L\"{u} system with the MSCDTM to demonstrate the efficiency and effectiveness of the proposed procedure.

Using Sălăgean differential operator, we study new subclasses of analytic functions. Coefficient inequalities and distortion theorems and extreme points of these classes are studied. Furthermore, integral means inequalities are obtained for the fractional derivatives of these classes.