جستجوی مقالات مرتبط با کلیدواژه "fractional derivative" در نشریات گروه "ریاضی"

In this study, we presented a computationally intensive alternative and a suitable time-fractional order model to further comprehend the transmission dynamics of Diphtheria and study the overall effects of some control measures on its transmission. Public awareness (U1), immediate treatment after being diagnosed (U2) and the combination of both controls (U3) are the three measures considered and all parameters and conditions that guarantee feasible of the proposed SEIR model: uniqueness and existence of solutions, the reproduction number, boundedness and positivity of solutions, global and local stability analysis of the disease-free equilibrium state was thoroughly analyzed and established, the Adam’s Bashforth predictor-corrector method was utilized for the numerical solution, More interestingly, analysis of the optimal control from simulations emphasized gradual elimination of the infection in the population and finally flattens the transmission curve and so health practitioner and concerned authorities are better educated about possible control measures and the overall combine effects of such measures

A unified explicit form for difference formulas to approximate fractional and classical derivatives is presented. The formula gives finite difference approximations for any classical derivative with a desired order of accuracy at any nodal point in computational domain. It also gives Gr¨unwald type approximations for fractional derivatives with arbitrary order of approximation at any nodal point. Thus, this explicit form unifies approximations of both types of derivatives. Moreover, for classical derivatives, it also provides various finite difference formulas such as forward, backward, central, staggered, compact, non-compact, etc. Efficient computations of the coefficients of the difference formulas are also presented leading to automating the solution process of differential equations with a given higher order accuracy. Some basic applications are presented to demonstrate the usefulness of this unified formulation.

The aim of this paper is to investigate the existence and uniqueness of solutions to uncertain fractional differential equations proposed by Canonical Liu’s process. To this end, we provide and prove a novel existence and uniqueness theorem for uncertain fractional differential equations under Local Lipschitz and monotone conditions is provided and proved. This result helps us to consider and analyze solutions to a wide range of nonlinear uncertain fractional differential equations driven by Canonical’s process to be considered and analyzed.

This article presents a parameter uniform convergence numerical scheme for solving time fractional order singularly perturbed parabolic convection-diffusion differential equations with a delay. We give a priori bounds on the exact solution and its derivatives obtained through the problem’s asymp-totic analysis. The Euler’s method on a uniform mesh in the time direction and the extended cubic B-spline method with a fitted operator on a uniform mesh in the spatial direction is used to discretize the problem. The fitting factor is introduced for the term containing the singular perturbation pa-rameter, and it is obtained from the zeroth-order asymptotic expansion of the exact solution. The ordinary B-splines are extended into the extended B-splines. Utilizing the optimization technique, the value of μ (free param-eter, when the free parameter μ tends to zero the extended cubic B-spline reduced to convectional cubic B-spline functions) is determined. It is also demonstrated that this method is better than some existing methods in the literature.

In this paper a new definitionn of fractional derivative and fractional integral in the sense ofconformable derivative type is presented. This form of definition shows that it is more compatible withclassical natural definition of derivative and is more convinient fractional derivative one. We will definethis for 0 ≤ α < 1 and n − 1 ≤ α < n and further, if α = 1 the definition coincides with the classicaldefinition of derivative of first order.

This paper presents the development of a series of fractional multi-step linear finite difference methods (FLMMs) designed to address fractional multi-delay pantograph differential equations of order $0 < \alpha \leq 1$. These $p$ FLMMs are constructed using fractional backward differentiation formulas of first and second orders, thereby facilitating the numerical solution of fractional differential equations. Notably, we employ accurate approximations for the delayed components of the equation, guaranteeing the retention of stability and convergence characteristics in the proposed $p$-FLMMs. To substantiate our theoretical findings, we offer numerical examples that corroborate the efficacy and reliability of our approach.

It is well known that the solution of fractional models proved to be a powerful tool in studying various problems which appear in the sciences of real life. In view of the fact that economic applications are accelerating at an amazing pace, and the large number of modeling in this speciality, it has expanded the number of problems. So, our contribution is based on finding generalized solutions of a fractional differential equation known for their applications in microeconomics and finance and creating an algorithm which allows us to estimate the coefficients of this type of equation. And to really illustrate our results we will choose a model known in the stochastic literature by COGARCH but with fractional derivative, to demonstrate the asymptotic behavior of the estimators, including the impact of fractional order on the space of stochastic differential equations.

In this work, we establish the existence of at least two positive solutions for a coupled system of $p$-Laplacian fractional-order boundary value problems. Establishing the existence of positive solutions to the problem is challenging for a variety of reasons, the most important of which is a lack of compatibility with the kernel. To address these issues, we have included the necessary conditions for overcoming certain methodological hurdles on the kernel as well as adapting to the problem's nature of positivity. The method is based on the AH functional fixed point theorem.

‎The main purpose of this paper is to develop and analyse a fractional SIQR epidemic model with Caputo-Fabrizio derivative‎. ‎It is shown that the model to have a disease-free and an endemic equilibrium point‎. ‎Some conditions are derived for the‎ existence and stability of these equilibrium points‎. ‎Finally‎, ‎three-step fractional Adams-Bashforth method applied to the model and some numerical simulations are illustrate the results‎.

Covid-19 disease is a respiratory illness caused by SARS-Cov-2 and poses a serious public health risk. It usually spread from person-to-person. The fractional- order of covid-19 was determined and basic reproduction number using the next generation matrix was calculated. The stability of disease-free equilibrium and endemic equilibrium of the model were investigated. Also, sensitivity analysis of the reproduction number with respect to the model parameters were carried out. It was observed that in the absence of infected persons, disease free equilibrium is achievable and is asymptotically stable.Numerical simulations were presented graphically. The results of the model analysis indicated that $R_{0}$ $\mathrm{<}$ 1 is adequate enough to reducing the spread of disease and disease persevere in the population when $R_{0}$ $\mathrm{>}$ 1 The numerical results showed that effective vaccination of the population helps in curtailing the spread of the viral disease.In order to know whether the disease may die out or persist, basic reproduction number, $R_{0}$ was obtained using Next Generation Matrix Method. It was observed that the value of $R_{0}$ is high when the depletion of awareness programme is high while the value of $R_{o}$ is very low when the rate of implementation of awareness programme is high. So, neglecting the implementation of awareness program can have serious effect on the population. The model shows the implementation of awareness program is the key eradication to the pandemic.

This article discusses the replicating kernel interpolation collocation method related to Jacobi polynomials to solve a class of fractional system of equations. The reproducing kernel function that is executed as an (RKM) was first created in the form of Jacobi polynomials. To prevent Schmidt orthogonalization, researchers compare the numerical solutions achieved by varying the parameter value. Through various numerical examples, it is demonstrated that this technique is practical and precise.

This paper deals with the existence of solutions to the system of nonlinear infinite-point fractional order boundary value problems by an application of n-best proximity point theorem in a complete metric space. Further, we study Hyers-Ulam stability of the addressed system. An appropriate example is given to demonstrate the established results.

In this paper, we discuss atomic solutions of the second-order abstract Cauchy problem of conformable fractional type u(2α)(t)+Bu(α)(t)+Au(t)u(0)u(α)(0)===f(t)u0,u(α)0, % where A,B are closed linear operators on a Banach space X, f :[0,∞)→X \ is continuous and u is a continuously differentiable function on [0,∞). Some new results on atomic solutions using tensor product technique are obtained.

Stochastic differential equations (SDEs) have been applied by engineers and economists because it can express the behavior of stochastic processes in compact expressions. In this paper, by using Grunwald-Letnikov fractional derivative, the stochastic differential model is improved. Two numerical examples are presented to show efficiency of the proposed model. A numerical optimization approach based on least square approximation is applied to determine the order of the fractional derivative. Numerical examples show that the proposed model works better than the SDE to model stochastic processes with memory.

In this study, a radial basis functions (RBFs) method for solving nonlinear timeand space-fractional Fokker-Planck equation is presented. The time-fractional derivative is of the Caputo type, and the space-fractional derivatives are considered in the sense of Caputo or Riemann-Liouville. The Caputo and Riemann-Liouville fractional derivatives of RBFs are computed and utilized for approximating the spatial fractional derivatives of the unknown function. Also, in each time step, the time-fractional derivative is approximated by the high order formulas introduced in [6], and then a collocation method is applied. The centers of RBFs are chosen as suitable collocation points. Thus, in each time step, the computations of fractional Fokker-Planck equation are reduced to a nonlinear system of algebraic equations. Several numerical examples are included to demonstrate the applicability, accuracy, and stability of the method. Numerical experiments show that the experimental order of convergence is 4 − α where α is the order of time derivative.

In this paper, a hybrid function method based on combination of block-pulse functions and Legendre polynomials is used for solving a fractional model of HIV infection of CD4+ T cells in which fractional derivatives are considered in Caputo sense. Using this method, the system of fractional ordinary differential equations which is the mathematical model for the fractional model of HIV infection of CD4+T cells, is reduced into a system of algebraic equations. This system can be solved by a numerical method. Also, convergence analysis of the method is studied and an upper bound of the error is obtained. To show efficiency and accuracy the proposed method, a numerical example is simulated and some comparisons and results are reported. In this paper, a hybrid function method based on combination of block-pulse functions and Legendre polynomials is used for solving a fractional model of HIV infection of CD4+ T cells in which fractional derivatives are considered in Caputo sense. Using this method, the system of fractional ordinary differential equations which is the mathematical model for the fractional model of HIV infection of CD4+T cells, is reduced into a system of algebraic equations. This system can be solved by a numerical method. Also, convergence analysis of the method is studied and an upper bound of the error is obtained. To show efficiency and accuracy the proposed method, a numerical example is simulated and some comparisons and results are reported.

In this paper, a numerical method is developed and analyzed for solving a class of fractional optimal control problems (FOCPs) with vector state and control functions using polynomial approximation. The fractional derivative is considered in the Caputo sense. To implement the proposed numerical procedure, the Ritz spectral method with Bernoulli polynomials basis is applied. By applying the Bernoulli polynomials and using the numerical estimation of the unknown functions, the FOCP is reduced to solve a system of algebraic equations. By rigorous proofs, the convergence of the numerical method is derived for the given FOCP. Moreover, a new fractional operational matrix compatible with the proposed spectral method is formed to ease the complexity in the numerical computations. At last, several test problems are provided to show the applicability and effectiveness of the proposed scheme numerically.

In this paper, we establish the existence of denumerably many positive solutions for singular iterative system of fractional order boundary value problem involving Riemann--Liouville integral boundary conditions with increasing homeomorphism and positive homomorphism operator by using H"{o}lder's inequality and Krasnoselskii's cone fixed point theorem in a Banach space.

In this work, we introduce and investigate an interesting operator Q ν λ based on fractional derivative which is introduced by Owa and Srivastava in [10]. We consider a new technique to prove our results and then, we introduce two subclasses of analytic functions in the open unit disk U concerning with this operator. Some results such as inclusion relations, subordination properties, integral preserving properties and argument estimate are investigated.