Coronavirus disease (COVID-19) is an infectious disease caused by a newly discovered coronavirus. This paper provides a numerical solution for the mathematical model of the novel coronavirus by the application of alternative Legendre polynomials to find the transmissibility of COVID-19. The mathematical model of the present problem is a system of differential equations. The goal is to convert this

The main aim of this paper is to introduce the concept of \(\mathcal{N}_{b}\)-cone metric spaces over a Banach algebra as a generalization of \(\mathcal{N}\)-cone metric spaces over a Banach algebra and b-metric spaces. Also, we study some coupled common fixed point theorems for generalized Lipschitz mappings in this framework. Finally, we give an example and an application to the existence of solutions

In this paper, a novel coronavirus (2019-nCov) mathematical model with modified parameters is presented. This model consists of six nonlinear fractional order differential equations. Optimal control of the suggested model is the main objective of this work. Two control variables are presented in this model to minimize the population number of infected and asymptotically infected people. Necessary optimality

The aim of the present study is to consider a heroin epidemic model with age-structure only in the active heroin users. The model was formulated with the help of available literature on heroin epidemic. Instead of treatment as a class, we incorporated recovered population and considered treatment as a control variable and thus a control problem is presented for further analysis. The techniques of weak

This paper deals with a general SEIR model for the coronavirus disease 2019 (COVID-19) with the effect of time delay proposed. We get the stability theorems for the disease-free equilibrium and provide adequate situations of the COVID-19 transmission dynamics equilibrium of present and absent cases. A Hopf bifurcation parameter τ concerns the effects of time delay and we demonstrate that the locally

Alcoholism is a social phenomenon that affects all social classes and is a chronic disorder that causes the person to drink uncontrollably, which can bring a series of social problems. With this motivation, a delayed drinking model including five subclasses is proposed in this paper. By employing the method of characteristic eigenvalue and taking the temporary immunity delay for alcoholics under treatment

This manuscript considers a nonlinear coupled system under nonsingular kernel type derivative. The considered problem is investigated from two aspects including existence theory and approximate analytical solution. For the concerned qualitative theory, some fixed point results are used. While for approximate solution, the Laplace transform coupled with Adomian method is applied. Finally, by a pertinent

Nonlinear Schrödinger’s equation and its variation structures assume a significant job in soliton dynamics. The soliton solutions of space-time fractional Fokas–Lenells equation with a relatively new definition of local M-derivative have been recovered by utilizing improved \(\tan (\frac{\phi (\eta )}{2})\)-expansion method and generalized projective Riccati equation method. The obtained solutions

In this study, the double Laplace Adomian decomposition method and the triple Laplace Adomian decomposition method are employed to solve one- and two-dimensional time-fractional Navier–Stokes problems, respectively. In order to examine the applicability of these methods some examples are provided. The presented results confirm that the proposed methods are very effective in the search of exact and

An expectation for optimal integrated pest management is that the instantaneous numbers of natural enemies released should depend on the densities of both pest and natural enemy in the field. For this, a generalised predator–prey model with nonlinear impulsive control tactics is proposed and its dynamics is investigated. The threshold conditions for the global stability of the pest-free periodic solution

The objective of this paper is to present two numerical techniques for solving generalized fractional differential equations. We develop Haar wavelets operational matrices to approximate the solution of generalized Caputo–Katugampola fractional differential equations. Moreover, we introduce Green–Haar approach for a family of generalized fractional boundary value problems and compare the method with

In the paper, a high-order alternating direction implicit (ADI) algorithm is presented to solve problems of unsteady convection and diffusion. The method is fourth- and second-order accurate in space and time, respectively. The resulting matrix at each ADI computation can be obtained by repeatedly solving a penta-diagonal system which produces a computationally cost-effective solver. We prove that

In this paper, we study a modified extragradient method for computing a common solution to the split equilibrium problem and fixed point problem of a nonexpansive semigroup in real Hilbert spaces. The weak and strong convergence characteristics of the proposed algorithm are investigated by employing suitable control conditions in such a setting of spaces. As a consequence, we provide a simplified analysis

In this paper, we present a numerical simulation to study a fractional-order differential system of a glioblastoma multiforme and immune system. This numerical simulation is based on spectral collocation method for tackling the fractional-order differential system of a glioblastoma multiforme and immune system. We introduce new shifted fractional-order Legendre orthogonal functions outputted by Legendre

In this work, a time-fractional diffusion problem with a time-space dependent diffusivity is considered. The solution of such a problem has a weak singularity at the initial time \(t=0\). Based on the L1 scheme in time on a graded mesh and the conforming finite element method in space on a uniform mesh, the fully discrete L1 conforming finite element method (L1 FEM) of a time-fractional diffusion problem

In this paper, a mathematical model for COVID-19 that involves contact tracing is studied. The contact tracing-induced reproduction number \(\mathcal{R}_{q}\) and equilibrium for the model are determined and stabilities are examined. The global stabilities results are achieved by constructing Lyapunov functions. The contact tracing-induced reproduction number \(\mathcal{R}_{q}\) is compared with the

Recently, the nth Lah–Bell number was defined as the number of ways a set of n elements can be partitioned into nonempty linearly ordered subsets for any nonnegative integer n. Further, as natural extensions of the Lah–Bell numbers, Lah–Bell polynomials are defined. We study Lah–Bell polynomials with and without the help of umbral calculus. Notably, we use three different formulas in order to express

In this paper, we give and study the concept of n-polynomial \((s,m)\)-exponential-type convex functions and some of their algebraic properties. We prove new generalization of Hermite–Hadamard-type inequality for the n-polynomial \((s,m)\)-exponential-type convex function ψ. We also obtain some refinements of the Hermite–Hadamard inequality for functions whose first derivatives in absolute value at

Environmental factors, such as humidity, precipitation, and temperature, have significant impacts on the spread of the new strain coronavirus COVID-19 to humans. In this paper, we use a stochastic epidemic SIRC model, with cross-immune class and time-delay in transmission terms, for the spread of COVID-19. We analyze the model and prove the existence and uniqueness of positive global solution. We deduce

The notion of m-polynomial convex interval-valued function \(\Psi =[\psi ^{-}, \psi ^{+}]\) is hereby proposed. We point out a relationship that exists between Ψ and its component real-valued functions \(\psi ^{-}\) and \(\psi ^{+}\). For this class of functions, we establish loads of new set inclusions of the Hermite–Hadamard type involving the ρ-Riemann–Liouville fractional integral operators. In

The current effort is devoted to investigating and exploring the stochastic nonlinear mathematical pandemic model to describe the dynamics of the novel coronavirus. The model adopts the form of a nonlinear stochastic susceptible-infected-treated-recovered system, and we investigate the stochastic reproduction dynamics, both analytically and numerically. We applied different standard and nonstandard

Recently, special functions of fractional order calculus have had many applications in various areas of mathematical analysis, physics, probability theory, optimization theory, graph theory, control systems, earth sciences, and engineering. Very recently, Zayed et al. (Mathematics 8:136, 2020) introduced the shifted Legendre-type matrix polynomials of arbitrary fractional orders and their various applications

In this study, we examine the stabilization of fractional-order chaotic nonlinear dynamical systems with model uncertainties and external disturbances. We used the sliding mode controller by a new approach for controlling and stabilization of these systems. In this research, we replaced a continuous function with the sign function in the controller design and the sliding surface to suppress chattering

In this paper, a new numerical algorithm for solving the time fractional convection–diffusion equation with variable coefficients is proposed. The time fractional derivative is estimated using the \(L_{1}\) formula, and the spatial derivative is discretized by the sinc-Galerkin method. The convergence analysis of this method is investigated in detail. The numerical solution is \(2-\alpha\) order accuracy

A simple deterministic epidemic model for tuberculosis is addressed in this article. The impact of effective contact rate, treatment rate, and incomplete treatment versus efficient treatment is investigated. We also analyze the asymptotic behavior, spread, and possible eradication of the TB infection. It is observed that the disease transmission dynamics is characterized by the basic reproduction ratio

In this article, some high-order compact finite difference schemes are presented and analyzed to numerically solve one- and two-dimensional time fractional Schrödinger equations. The time Caputo fractional derivative is evaluated by the L1 and L1-2 approximation. The space discretization is based on the fourth-order compact finite difference method. For the one-dimensional problem, the rates of the

In this paper, certain Hermite–Jensen–Mercer type inequalities are proved via conformable integrals of arbitrary order. We establish some different and new fractional Hermite–Hadamard–Mercer type inequalities for a differentiable function f whose derivatives in the absolute values are convex.

In this article, we give a definition and discuss several properties of the δ-β-Gabor integral operator in a class of locally integrable Boehmians. We derive delta sequences, convolution products and establish a convolution theorem for the given δ-β-integral. By treating the delta sequences, we derive the necessary axioms to elevate the δ-β-Gabor integrable spaces of Boehmians. The said generalized

When working with mathematical models, to keep the model errors as small as possible, a special system of linear equations is constructed whose solution vector yields accurate discretized values for the exact solution of the second-order linear inhomogeneous ordinary differential equation (ODE). This case involves a 1D spatial variable x with an arbitrary coefficient function \(\kappa (x)\) and an

The present article addresses the concept of p-convex functions on fractal sets. We are able to prove a novel auxiliary result. In the application aspect, the fidelity of the local fractional is used to establish the generalization of Simpson-type inequalities for the class of functions whose local fractional derivatives in absolute values at certain powers are p-convex. The method we present is an

In this paper, by making use of the familiar q-difference operators \(D_{q}\) and \(D_{q^{-1}}\), we first introduce two homogeneous q-difference operators \(\mathbb{T}(\mathbf{a},\mathbf{b},cD_{q})\) and \(\mathbb{E}(\mathbf{a},\mathbf{b}, cD_{q^{-1}})\), which turn out to be suitable for dealing with the families of the generalized Al-Salam–Carlitz q-polynomials \(\phi_{n}^{(\mathbf{a},\mathbf{b})}(x

The aim of the paper is to derive certain formulas involving integral transforms and a family of generalized Wright functions, expressed in terms of the generalized Wright hypergeometric function and in terms of the generalized hypergeometric function as well. Based on the main results, some integral formulas involving different special functions connected with the generalized Wright function are explicitly

In the present work, a numerical technique for solving a general form of nonlinear fractional order integro-differential equations (GNFIDEs) with linear functional arguments using Chebyshev series is presented. The recommended equation with its linear functional argument produces a general form of delay, proportional delay, and advanced non-linear arbitrary order Fredholm–Volterra integro-differential

In this paper, we study the dynamics property of a stochastic HIV model with Beddington–DeAngelis functional response. It has a unique uninfected steady state. We prove that the model has a unique global positive solution. Furthermore, if the basic reproductive number is not larger than 1, the asymptotic behavior of the solution is stochastically stable. Otherwise, it fluctuates randomly around the

This paper investigates the existence of solutions to subquadratic operator equations with convex nonlinearities and resonance by means of the index theory for self-adjoint linear operators developed by Dong and dual least action principle developed by Clarke and Ekeland. Applying the results to subquadratic convex Hamiltonian systems satisfying several boundary value conditions including Bolza boundary

We provide a SEIR epidemic model for the spread of COVID-19 using the Caputo fractional derivative. The feasibility region of the system and equilibrium points are calculated and the stability of the equilibrium points is investigated. We prove the existence of a unique solution for the model by using fixed point theory. Using the fractional Euler method, we get an approximate solution to the model

To forecast the spread tendency of the COVID-19 in China and provide effective strategies to prevent the disease, an improved SEIR model was established. The parameters of our model were estimated based on collected data that were issued by the National Health Commission of China (NHCC) from January 10 to March 3. The model was used to forecast the spread tendency of the disease. The key factors influencing

We study the SEIR epidemic model for the spread of AH1N1 influenza using the Caputo–Fabrizio fractional-order derivative. The reproduction number of system and equilibrium points are calculated, and the stability of the disease-free equilibrium point is investigated. We prove the existence of solution for the model by using fixed point theory. Using the fractional Euler method, we get an approximate

This paper investigates a new model on coronavirus-19 disease (COVID-19) with three compartments including susceptible, infected, and recovered class under Mittag-Leffler type derivative. The mentioned derivative has been introduced by Atangana, Baleanu, and Caputo abbreviated as \((\mathcal{ABC})\). Upon utilizing fixed point theory, we first prove the existence of at least one solution for the considered

This paper is concerned with traveling curved fronts of bistable reaction–diffusion equations with nonlinear convection in a two-dimensional space. By constructing super- and subsolutions, we establish the existence of traveling curved fronts. Furthermore, we show that the traveling curved front is globally asymptotically stable.

It is known that every solution to the second-order difference equation \(x_{n}=x_{n-1}+x_{n-2}=0\), \(n\ge 2\), can be written in the following form \(x_{n}=x_{0}f_{n-1}+x_{1}f_{n}\), where \(f_{n}\) is the Fibonacci sequence. Here we find all the homogeneous linear difference equations with constant coefficients of any order whose general solution have a representation of a related form. We also

We propose and analyze a new type iterative algorithm to find a common solution of split monotone variational inclusion, variational inequality, and fixed point problems for an infinite family of nonexpansive mappings in the framework of Hilbert spaces. Further, we show that a sequence generated by the algorithm converges strongly to common solution. Furthermore, we list some consequences of our established

This paper presents theoretical results on the finite-time synchronization of delayed memristive neural networks (MNNs). Compared with existing ones on finite-time synchronization of discontinuous NNs, we directly regard the MNNs as a switching system, by introducing a novel analysis method, new synchronization criteria are established without employing differential inclusion theory and non-smooth

In this paper, a fast collocation method is developed for a two-dimensional variable-coefficient linear nonlocal diffusion model. By carefully dealing with the variable coefficient in the integral operator and then analyzing the structure of the coefficient matrix, we can reduce the computational operations in each Krylov subspace iteration from \(O(N^{2})\) to \(O(N\log N)\) and the memory requirement

We introduce an extension of Darbo’s fixed point theorem via a measure of noncompactness in a Banach space. By using our extension we study the existence of a solution for a system of nonlinear integral equations, which is an extended result of (Aghajani and Haghighi in Novi Sad J. Math. 44(1):59–73, 2014). We give an example to show the specified existence results.

This study investigates the solutions of an impulsive fractional differential equation incorporated with a pantograph. This work extends and improves some results of the impulsive fractional differential equation. A differential equation of an impulsive fractional pantograph with a more general anti-periodic boundary condition is proposed. By employing the well-known fixed point theorems of Banach

This investigation is devoted to the study of a certain class of coupled systems of higher-order Hilfer fractional boundary value problems at resonance. Combining the coincidence degree theory with the Lipschitz-type continuity conditions on nonlinearities, we present some existence and uniqueness criteria. Finally, to practically implement the obtained theoretical criteria, we give an illustrative

Let f and g be two nonconstant meromorphic functions. Shared value problems related to f and g are investigated in this paper. We give sufficient conditions in terms of weighted value sharing which imply that f is a linear transformation or inversion transformation of g. We also investigate the uniqueness problem of meromorphic functions with their difference operators and derivatives sharing some

The dynamical attitude of the transmission for the nerve impulses of a nervous system, which is mathematically formulated by the Atangana–Baleanu (AB) time-fractional FitzHugh–Nagumo (FN) equation, is computationally and numerically investigated via two distinct schemes. These schemes are the improved Riccati expansion method and B-spline schemes. Additionally, the stability behavior of the analytical

We study a fractional-order model for the anthrax disease between animals based on the Caputo–Fabrizio derivative. First, we derive an existence criterion of solutions for the proposed fractional \(\mathcal {CF}\)-system of the anthrax disease model by utilizing the Picard–Lindelof technique. By obtaining the basic reproduction number \(\mathcal{R}_{0}\) of the fractional \(\mathcal{CF}\)-system we

We investigate non-Gaussian noise second-order filtering and fixed-order smoothing problems for non-Gaussian stochastic discrete systems with packet dropouts. We present a novel Kalman-like nonlinear non-Gaussian noise estimation approach based on the packet dropout probability distribution and polynomial filtering technique. By means of properties of Kronecker product we first introduce a second-order

We investigate the existence of different types of nonoscillatory solutions to a class of higher-order nonlinear neutral dynamic equations on a time scale. Two examples are provided to show the significance of the conclusions.

In this paper, a novel coronavirus infection system with a fuzzy fractional differential equation defined in Caputo’s sense is developed. By using the fuzzy Laplace method coupled with Adomian decomposition transform, numerical results are obtained for better understanding of the dynamical structures of the physical behavior of COVID-19. Such behavior on the general properties of RNA in COVID-19 is

A generalized nonisospectral heat integrable hierarchy with three dependent variables is singled out. A Bäcklund transformation of a resulting isospectral integrable hierarchy is produced by converting the usual Lax pair into the Lax pairs in Riccati forms. In addition, an expanding integrable model is also worked out by making use of a set of linear spectral problems which are introduced via a high-dimensional

We discuss some existence criteria for a new category of the Caputo conformable differential inclusion furnished with four-point mixed Riemann–Liouville conformable integro-derivative boundary conditions. In this way, we employ some analytical techniques on α-ψ-contractive mappings and operators having the approximate endpoint property to reach desired theoretical results. Finally, we provide an example

In the present paper, we aim to extend the Hurwitz–Lerch zeta function \(\varPhi _{\delta ,\varsigma ;\gamma }(\xi ,s,\upsilon ;p)\) involving the extension of the beta function (Choi et al. in Honam Math. J. 36(2):357–385, 2014). We also study the basic properties of this extended Hurwitz–Lerch zeta function which comprises various integral formulas, a derivative formula, the Mellin transform, and

In this paper we first obtain various new forms of the q-analogue of the I-function satisfying Truesdell’s ascending and descending \(F_{q}\)-equation. Then we use these forms to obtain new generating functions for the q-analogue of the I-function. Some particular cases of these results in terms of the q-analogue of the I-function, H-function and G-function have also been obtained.

In this manuscript, we obtain sufficient conditions required for the existence of solution to the following coupled system of nonlinear fractional order differential equations: $$ \begin{gathered} D^{\gamma}\omega(\ell)= \mathcal{F} \bigl( \ell,\omega(\lambda\ell), \upsilon(\lambda\ell) \bigr), \\ D^{\delta}\upsilon(\ell)=\mathcal{\overline{F}} \bigl(\ell,\omega ( \lambda\ell), \upsilon(\lambda\ell)

Mosquitoes play an important role in the spread of mosquito-borne diseases. Considering the sensitivity of mosquitoes’ aquatic stage to the seasonal shift, in this paper, we present a seasonally forced mosquito-borne epidemic model by incorporating mosquitoes’ aquatic stage (eggs, larvae, and pupae) and seasonal shift factor, which is a periodic discontinuous differential system. Firstly, some sufficient

In this work, we construct a Durrmeyer type modification of the τ-Baskakov operators depends on two parameters \(\alpha >0\) and \(\tau \in [0,1]\). We derive the rate of approximation of these operators in a weighted space and also obtain a quantitative Voronovskaja type asymptotic formula as well as a Grüss Voronovskaya type approximation.