2021 June - 33 articles
In the three-dimensional open rectangular domain, the problem of the identification of the redefinition function for a partial differential equation with Gerasimov–Caputo-type fractional operator, degeneration, and integral form condition is consider...
We present a general series representation formula for the local solution of the Bernoulli equation with Caputo fractional derivatives. We then focus on a generalization of the fractional logistic equation and present some related numerical simulations.
This article aims to introduce an efficient simulation to obtain the solution for a dynamical–biological system, which is called the Lotka–Volterra system, involving predator–prey equations. The finite element method (FEM) is employed to solve this p...
In this paper, a novel escape-time algorithm is proposed to calculate the connectivity’s degree of Julia sets generated from polynomial maps. The proposed algorithm contains both quantitative analysis and visual display to measure the connectivity of...
In this article, we established a new version of generalized fractional Hadamard and Fejér–Hadamard type integral inequalities. A fractional integral operator (FIO) with a non-singular function (multi-index Bessel function) as its kernel and monotone...
This paper is concerned with establishing novel expressions that express the derivative of any order of the orthogonal polynomials, namely, Chebyshev polynomials of the sixth kind in terms of Chebyshev polynomials themselves. We will prove that these...
The existence of solutions for a class of nonlinear neutral Hadamard-type fractional integro-differential equations with infinite delay is researched in this paper. By constructing an appropriate normed space and utilizing the Banach contraction prin...
In recent years, different experimental works with molecular simulation techniques have been developed to study the transport of plasma-generated reactive species in liquid layers. Here, we improve the classical transport model that describes the mol...
Phytoplankton movement patterns and swimming behavior are important and basic topics in aquatic biology. Heavy tail distribution exists in diverse taxa and shows theoretical advantages in environments. The fat tails in the movement patterns and swimm...
We present an analytic solvability of a class of Langevin differential equations (LDEs) in the asset of geometric function theory. The analytic solutions of the LDEs are presented by utilizing a special kind of fractal function in a complex domain, l...
In this paper, we study diffusion equations involving Hadamard-type time-fractional derivatives related to ultra-slow random models. We start our analysis using the abstract fractional Cauchy problem, replacing the classical time derivative with the...
Cement-based materials are widely utilized in infrastructure. The main product of hydrated products of cement-based materials is calcium silicate hydrate (C-S-H) gels that are considered as the binding phase of cement paste. C-S-H gels in Portland ce...
An alternative procedure for the implementation of fractional-order compensators is presented in this work. The employment of a curve-fitting-based approximation technique for the approximation of the compensator transfer function offers improved acc...
This study investigates the predictions of the real contact area for perfectly elastic rough surfaces using a boundary element method (BEM). Sample surface measurements were used in the BEM to predict the real contact area as a function of load. The...
Several extensions of the classical Mittag-Leffler function, including multi-parameter and multivariate versions, have been used to define fractional integral and derivative operators. In this paper, we consider a function of one variable with five p...
We shall discuss three methods of inverse Laplace transforms. A Sinc-Thiele approximation, a pure Sinc, and a Sinc-Gaussian based method. The two last Sinc related methods are exact methods of inverse Laplace transforms which allow us a numerical app...
In this paper, we define fractal bases and fractal frames of
In this paper, we consider a problem of continuity fractional-order for pseudo-parabolic equations with the fractional derivative of Caputo. Here, we investigate the stability of the problem with respect to derivative parameters and initial data. We...
Porous structures exhibiting randomly sized and distributed pores are required in biomedical applications (producing implants), materials science (developing cermet-based materials with desired properties), engineering applications (objects having co...
This work focuses on a kind of fractals Parrondo’s paradoxial phenomenon “deiconnected+diconnected=connected” in an alternated superior complex system
The contribution of this article is mainly to develop a new stochastic sequence forecasting model, which is also called the difference iterative forecasting model based on the Generalized Cauchy (GC) process. The GC process is a Long-Range Dependent...
A system of nonlinear fractional differential equations with the Riemann–Liouville fractional derivative is considered. Lipschitz stability in time for the studied equations is defined and studied. This stability is connected with the singularity of...
We considered relaxation, creep, dissipation, and hysteresis resulting from a six-parameter fractional constitutive model and its particular cases. The storage modulus, loss modulus, and loss factor, as well as their characteristics based on the ther...
Within this manuscript we generalize the two recently obtained results of O. Popescu and G. Stan, regarding the F-contractions in complete, ordinary metric space to 0-complete partial metric space and 0-complete metric-like space. As Popescu and Stan...
Mathematical models have been frequently studied in recent decades in order to obtain the deeper properties of real-world problems [...]
Stochastic fractal search (SFS) is a novel method inspired by the process of stochastic growth in nature and the use of the fractal mathematical concept. Considering the chaotic stochastic diffusion property, an improved dynamic stochastic fractal se...
It is possible to produce mobile phone worms, which are computer viruses with the ability to command the running of cell phones by taking advantage of their flaws, to be transmitted from one device to the other with increasing numbers. In our day, on...
The rapid growth of geographic information technologies in the field of processing and analysis of spatial data has led to a significant increase in the role of geographic information systems in various fields of human activity. However, solving comp...
In this paper, a class of time-space fractional stochastic delay control problems with fractional noises and Poisson jumps in a bounded domain is considered. The proper function spaces and assumptions are proposed to discuss the existence of mild sol...
In this article, we suggest the local analysis of a uni-parametric third and fourth order class of iterative algorithms for addressing nonlinear equations in Banach spaces. The proposed local convergence is established using an
The Koch curve was first described by the Swedish mathematician Helge von Koch in 1904 as an example of a continuous but nowhere differentiable curve. Such functions are now characterised as fractal since their graphs are in general fractal sets. Fur...
Optimal control of fractional order systems is a long established domain of fractional calculus. Nevertheless, it relies on equations expressed in terms of pseudo-state variables which raise fundamental questions. So in order remedy these problems, t...
The Baranyi–Roberts model describes the dynamics of the volumetric densities of two interacting cell populations. We randomize this model by considering that the initial conditions are random variables whose distributions are determined by using samp...
