Search

This paper investigates a fractional order SIR epidemic model with specific functional response and Holling type II treatment rate with fractional derivative in the Caputo sense. A thorough investigation of the existence, uniqueness, non-negativity and boundedness of the solutions has been performed in the beginning. Stability of the equilibria is analysed in the section next to it. Bifurcation analysis has also been carried out for the model. Finally, numerical simulations are used to support the theoretical findings. [ABSTRACT FROM AUTHOR]

• We investigate the common variational inclusion problem (CVIP) and offer a new parallel technique that combines viscosity modification with parallel inertial two-step forward-backward splitting approaches. • We prove the strongly convergent theorems in Hilbert spaces under some reasonable conditions. • For signal recovery problems requiring several filters, an extensive numerical examination is presented, with comparisons to the inertial parallel monotone hybrid method. • All of the numerical results show that the proposed algorithm solves the signal recovery problem and improves the quality of the observed signal significantly. In this paper, we introduce a new parallel algorithm by combining viscosity modification with parallel inertial two steps forward-backward splitting methods for approximating a solution of common inclusion problems. The strongly convergent theorems are established under some suitable conditions in Hilbert spaces. The applicability and advantages of the new parallel algorithm are presented by using to solve signal recovering problem in compressed sensing. The efficiency of the algorithm is shown by comparing it with some previous parallel algorithms. [ABSTRACT FROM AUTHOR]

Abstract: The main aim of this article is to extend the notion of strongly Cesàro summable and strongly lacunary summable real sequences to n-normed linear space valued (n-nls valued) difference sequences. Consequently we introduce the spaces |σ 1|(X,∇) and N θ (X,∇), respectively, where X is an n-normed space and ∇ is a difference operator. We investigate these spaces for completeness as well as for the relationship between these spaces. [Copyright &y& Elsevier]

In this work, we modify the inertial type parallel monotone hybrid algorithm with Armijo linesearch to solve common nonmonotone equilibrium problems. The weak convergence theorem is established under some suitable conditions in Hilbert spaces. Finally, the numerical example is shown to support our main result. The efficiencies of the proposed algorithm are presented by comparing with previously parallel algorithms in novel image restoration. It's illustrated that the proposed algorithm can increase deblurring quality when the subproblems are increasing. [ABSTRACT FROM AUTHOR]

The paper aims to investigate an HIV epidemic fractional model. The fractional derivatives are described in the sense of Caputo operator and Constant Proportional Caputo (CPC) operator, respectively. The existence of solution and stability analysis of the HIV mathematical model have been presented for the CPC fractional operator. The model is attempted to solve by using the fractional differential transform method and the Laplace Adomian decomposition method, respectively. The methods are further examined for different values of fractional order α. The findings show that the methods are effective for providing better results. [ABSTRACT FROM AUTHOR]

The study aims to develop a new mathematical model in order to explain the dynamics of viral infections in vivo such as HIV infection. The model includes three classes of cells, takes into account the cure of infected cells in latent period and also incorporates three modes of transmission. The mention modes are modeled by three general incidence functions covering several special cases available in the literature. The basic properties of the model as well as its stability analysis have been carried out rigorously. Further, an application is given and also numerical simulation results have been incorporated supporting the analytical results. [ABSTRACT FROM AUTHOR]

In this study, the model of the Ebola virus, which has been rapidly spreading in certain parts of Africa, was rearranged using the fractional derivative operator without a singular kernel proposed by Caputo and Fabrizio. It is aimed to obtain better results from the model using this approach of the model. In the first stage, the Ebola virus model was extended to the Caputo–Fabrizio fractional derivative operator. After, existence and uniqueness solutions were obtained for the fractional Ebola virus model via fixed-point theorem. Then, numerical solutions were obtained for the extended model by using Atangana and Owolabi new numerical approach via Adam-Basford method for the Caputo–Fabrizio fractional derivative. Finally, some numerical simulations were presented for different values of fractional order. [ABSTRACT FROM AUTHOR]

• The work of this paper aims to introduce the notions of statistical mean convergence, statistical measurable convergence, and statistical Lebesgue measurable convergence by using deferred Cesaro summability mean. The authors first established some fundamental results showing connections among the introduced notions. Then new versions of Korovkin-type approximation results with three algebraic test functions via deferred Cesaro statistical Lebesgue measurable convergence have been established. Several examples have also been given in the sequel to support the new ideas and major findings of the paper. Various summability methods are extremely useful in identifying unknown processes such as signals and images as well as approximating such processes. Thus, the results presented in this paper must find other applications than those presented in the paper. The work of this paper aims to introduce the notions of statistical mean convergence, statistical measurable convergence, and statistical Lebesgue measurable convergence by means of deferred Cesàro summability and apply them in Korovkin-type new approximations. We first established some fundamental results to understand the connections among them. Then we established new versions of Korovkin-type theorems with three algebraic test functions via deferred Cesàro statistical Lebesgue measurable convergence for sequences of measurable functions. Also, several examples have been given in the sequel to support our new ideas and findings. [ABSTRACT FROM AUTHOR]

• A new scheme for solving a type of singularly perturbed boundary value problem with a second order delay differential equation is presented. • Getting through the solution, Reproducing Kernel Hilbert Space (RKHS) method is implemented. • A construction of the reproducing kernel in Hilbert space satisfying the homogeneous nonlinear boundary conditions of the considered problem is presented. The present paper aims to carry out a new scheme for solving a type of singularly perturbed boundary value problem with a second order delay differential equation. Getting through the solution, we used Reproducing Kernel Hilbert Space (RKHS) method as an efficient approach to obtain the analytical solution for ordinary or partial differential equations that appear in vast areas of science and engineering. A key of this method is to keeping the continuous form of problems. Indeed, without discretizing the continuous problem, we change it to an equivalent iterative form and proving its convergence. Also, we will present a construction of the reproducing kernel in Hilbert space that satisfying the homogeneous nonlinear boundary conditions of the considered problem. Accuracy amount of absolute error with respect to different parameters of singularity has been studied for the performance of this method by solving several hardly nonlinear problems. Error estimation and convergence analysis show that the approximate results have uniform convergence to the continuous solutions. [ABSTRACT FROM AUTHOR]

This paper investigates the exact traveling wave solutions of the fractional model of the human immunodeficiency virus (HIV-1) infection for CD4 + T-cells. This model also treats with the effect of antiviral drug therapy. These solutions calculate both the boundary and initial conditions that allow employing the septic-B-spline scheme which is one of the most recent schemes in the numerical field. We use the obtained computational solutions via the modified Khater, the extended simplest equation, and sech–tanh methods through Atangana-Baleanu derivative operator. The comparison between the exact and numerical evaluated solutions is illustrated by some distinct sketches. The functioning of our numerical method is tested under three computational obtained solutions. [ABSTRACT FROM AUTHOR]

This article addresses the investigation of strict dissipativity synchronization for a class of static neural networks under an event-triggered scheme. An event-triggered scheme is recommended, it can upgrade the exhibition of system dynamics and diminishes the network communication burden at the same time. Firstly, an appropriate Lyapunov-Krasovskii functional (LKF) with double and triple integral terms with the details on both lower and upper bounds of the delay is completely designed. Secondly, under the single and double Auxillary function-based integral inequalities (SAFBII and DAFBII, respectively) and generalized free weight matrix approach, a new class of delay-dependent adequate condition is proposed, so that the error system is (Q , S , R) − γ − strict dissipative. A resilient distributed event-triggered control scheme is developed by this criterion in terms of linear matrix inequalities (LMIs). At last, simulation examples are provided to demonstrate the performance of the derived results. [ABSTRACT FROM AUTHOR]

• We consider a fractional extension of smoking model. • An iterative method is applied to obtain the solution of model. • Stability of proposed method is also discussed. • Numerical results are presented graphically. • Effect of fractional order on different kind of smokers is analysed. Smoking is a very challenging problem the world is facing every day. It contributes to deaths and major health problems to millions of people every year around the world. A lot of work has been devoted to study how to minimize smoking in the society. Here we study non-integer order smoking model using an iterative scheme which is combination of discretization of domain and short memory principle. We will also discuss stability of the proposed model and used iterative scheme. CPU time is listed in tabular to show the efficiency and figures are used to show behaviour of solution in long time. The proposed technique has high accuracy and low computational cost. Using figures fractional time behaviour of solution is also plotted. [ABSTRACT FROM AUTHOR]