Fractal and Fractional, Volume 6, Issue 9

In the present article, using the subordination principle, the authors employed certain generalized multiplier transform to define two new subclasses of analytic functions with respect to symmetric and conjugate points. In particular, bi-univalent co...

In this paper, we investigate the existence and multiplicity of solutions for a class of quasi-linear problems involving fractional differential equations in the $\chi$-fractional space ${\mathcal{H}}_{\kappa \left(x\right)}^{\gamma ,\beta ;\chi }\left(\mathsf{\Delta }\right)$. Using the Genus Theory,...

In this paper, we use the fixed-point index to establish positive solutions for a system of Riemann–Liouville type fractional-order integral boundary value problems. Some appropriate concave and convex functions are used to characterize couplin...

In this paper, we propose synchronous switching of rule and input to achieve H_∞ performance for an uncertain switched delay system with linear fractional perturbations. Our developed simple scheme utilizes the linear matrix inequality optimizat...

This paper deals with the design of a control system based on fractional order models and fractional order proportional-integral-derivative (FOPID) controllers and fractional-order proportional-integral (FOPI) controllers. The controller design takes...

Vortex rope is a common phenomenon in the draft tube of hydraulic turbines. It may cause strong pressure pulsation, noise, and strong vibration of the unit especially when it is helical. Therefore, the study of vortex rope is of great significance. I...

Concrete-face slabs are the primary anti-permeability structures of the concrete-face rockfill dam (CFRD), and the resistance of face slab concrete to permeability is the key factor affecting the operation and safety of CFRDs. Herein, the influences...

In this paper, the time fractional diffusion equations optimal control problem is solved by $3-\alpha$ order with uniform accuracy scheme in time and finite element method (FEM) in space. For the state and adjoint state equation, the piecewise l...

In this study, a rigorous mathematical approach used to compute an effective diameter based on particle size distribution (PSD) has been presented that can predict the hydraulic conductivity of granular soils with enhanced rigor. The PSD was discreti...

A new control strategy is proposed to suppress earthquake-induced vibrations on uncertain building structures. The control strategy embeds fuzzy logic in a fractional-order (FO) proportional derivative (FOPD) controller. A new improved FO particle sw...

In this paper, we introduce a new fractional-in-space modified phase-field crystal equation based on the $L^2$-gradient flow approach, where the mass of atoms is conserved by using a nonlocal Lagrange multiplier. To solve the $L^2$-gradient flow-based frac...

In this paper, an efficient prediction model based on the fractional generalized Pareto motion (fGPm) with Long-Range Dependent (LRD) and infinite variance characteristics is proposed. Firstly, we discuss the meaning of each parameter of the generali...

This article seeks to show a general framework of the cubic polynomial spline functions for developing a computational technique to solve the space-fractional Fisher’s equation. The presented approach is demonstrated to be conditionally stable...

The fractional Langevin equation is a very effective mathematical model for depicting the random motion of particles in complex viscous elastic liquids. This manuscript is mainly concerned with a class of nonlinear fractional Langevin equations invol...

In the present paper, PT-symmetric extension of the fifth-order Korteweg-de Vries-like equation are investigated. Several special equations with PT symmetry are obtained by choosing different values, for which their symmetries are obtained simultaneo...

This paper deals with a class of nonlinear fractional Sturm–Liouville boundary value problems. Each sub equation in the system is a fractional partial equation including the second kinds of Fredholm integral equation and the p-Laplacian operato...

This survey paper is devoted to succinctly reviewing the recent progress in the field of oscillation theory for linear and nonlinear fractional differential equations. The paper provides a fundamental background for all interested researchers who wou...

Destruction pattern analysis of building materials subjected to fire provide the basis for strengthening, restoring the bearing capacity, and optimizing the function of the building structure. The surface cracking and fractal characteristics of calci...

The aim of this paper is to investigate the following non local p-Laplacian problem with data a bounded Radon measure $\vartheta \in M_b\left(\mathsf{\Omega }\right)$: ${(-\mathsf{\Delta })}_p^{s}u=\vartheta \mathrm{in}\mathsf{\Omega },$ with vanishing conditions outside $\mathsf{\Omega },$ and where $s\in (0,1),2-\frac{s}{N}<p\le N.$ An existence result is provided, and some...

Rock permeability, defined as the ability of fluid to flow through the rocks, is one of the most important properties of rock. Many researchers have developed models to predict the permeability of rock from the porosity and pore size based on the mer...

To solve the issues with conventional level set segmentation algorithms, which are sensitive to the initial contours and less noise-resistant, a segmentation model based on the coupling of texture information and structural information is developed....