Fractal and Fractional, Volume 7, Issue 7

The concept of convexity is fundamental in order to produce various types of inequalities. Thus, convexity and integral inequality are closely related. The objectives of this paper are to present a new class of up and down convex fuzzy number valued...

In this paper, a mixed-order image denoising algorithm containing fractional-order and high-order regularization terms is proposed, which effectively suppresses the staircase effect generated by the TV model and its variants while better preserving t...

The present manuscript is devoted to investigating some existence and uniqueness results on fixed points by employing generalized contractions in the context of metric space endued with a weak class of transitive relation. Our results improve, modify...

A fully discrete space-time finite element method for the fractional Ginzburg–Landau equation is developed, in which the discontinuous Galerkin finite element scheme is adopted in the temporal direction and the Galerkin finite element scheme is...

The Jeffreys-type heat conduction equation with flux precedence describes the temperature of diffusive hot electrons during the electron–phonon interaction process in metals. In this paper, the deformation resulting from ultrafast surface heati...

In this article, the security control problem of discrete-time fractional-order networked systems under denial-of-service (DoS) attacks is considered. A practically applicable finite-dimensional control strategy will be developed for fractional-order...

One of the most popular controllers for the automatic voltage regulator (AVR) in maintaining the voltage level of a synchronous generator is the fractional-order proportional–integral-derivative (FOPID) controller. Unfortunately, tuning the FOP...

This work investigates a weighted Banach space second order pantograph fractional differential equation. The considered equation is of second order, expressed in terms of the Caputo–Hadamard fractional operator, and constructed in a general man...

In this investigation, weighted psi-Caputo fractional derivatives are applied to analyze the solution of fractional pantograph problems with boundary conditions. We establish the existence of solutions to the indicated pantograph equations as well as...

In this paper, we introduce a space-fractional version of the molecular beam epitaxy (MBE) model without slope selection to describe super-diffusion in the model. Compared to the classical MBE equation, the spatial discretization is an important issu...