Fractal and Fractional, Volume 6, Issue 8

Among the numerous applications of the theory of fractional calculus in almost all applied sciences, applications in numerical analysis and various fields of physics and engineering stand out [...]

This paper initiates a study on the existence and approximate controllability for a type of non-instantaneous impulsive stochastic evolution equation (ISEE) excited by fractional Brownian motion (fBm) with Hurst index 0<H<1/2. First, to overcom...

We present a finite difference/spectral method for the two-dimensional generalized time fractional cable equation by combining the second-order backward difference method in time and the Galerkin spectral method in space with Legendre polynomials. Th...

The time-fractional Cattaneo equation is an equation where the fractional order α∈(1,2) has the capacity to model the anomalous dynamics of physical diffusion processes. In this paper, we consider an efficient scheme for solving such an eq...

In our present investigation, a subclass of starlike function Sn−1,L* connected with a domain bounded by an epicycloid with n−1 cusps was considered. The main work is to investigate some coefficient inequalities, and second and third Hankel determina...

Motivated by the recent interest in generalized fractional order operators and their applications, we consider some classes of integro-differential initial value problems based on derivatives of the Riemann–Liouville and Caputo form, but with n...

A new auxiliary result pertaining to twice (q1,q2)-differentiable functions is derived. Using this new auxiliary result, some new versions of Hermite–Hadamard’s inequality involving the class of generalized m-convex functions are obtained. Finally, t...

We study a class of nonlinear fractional differential equations with multiple delays, which is represented by the Voigt creep fractional model of viscoelasticity. We discuss two Voigt models, the first being linear and the second being nonlinear. The...

This paper mainly considers the parameter estimation problem for several types of differential equations controlled by linear operators, which may be partial differential, integro-differential and fractional order operators. Under the idea of data-dr...

This paper proposes an algorithm and hardware realization of generalized chaotic systems using fractional calculus and rotation algorithms. Enhanced chaotic properties, flexibility, and controllability are achieved using fractional orders, a multi-sc...