Computational Methods for Differential Equations

In this paper, we present a new fractional-order financial system (FOFS) with the new parameters. We study the synchronization for commensurate order of the fractional-order financial system with disturbance observer (FOFSDO) on the new parameters. Also, the sensitivity analysis of the synchronization error was investigated by using the feedback control technique for the FOFSDO. The stability of the used method demonstrates by Lyapunov stability theorem. Numerical simulations are presented to ensure the validity and influence of the target feedback control design in the presence of extrinsic bounded unknown disturbance.

Malek Karimian

Bashir Naderi

Yousef Edrisi Tabriz

Computational methods for differential equations

Sensitivity analytic and synchronization of a new fractional-order financial system

新分数阶金融系统的敏感性分析与同步

The basic motivation of the present study is to apply the local fractional Sumudu variational iteration method (LFSVIM) for solving nonlinear wave-like equations with variable coefficients and within local fractional derivatives. The derivatives operators are taken in the local fractional sense. The results show that the LFSVIM is an appropriate method to find non-differentiable solutions for similar problems. The results of the solved examples showed the flexibility of applying this method and its ability to reach accurate results even with these new differential equations.

Djelloul Ziane

Mountassir Hamdi Cherif

Kacem Belghaba

Fethi Bin Muhammad Belgacem

An accurate method for nonlinear local fractional Wave-Like equations with variable coefficients

一种求解含变系数非线性局部分数波状方程的精确方法

In this paper, we first construct Alpert wavelet system and propose a computational method for solving a fractional nonlinear Fredholm integro-differential equation. Then we create an operational matrix of fractional integration and use it to simplify the equation to a system of algebraic equations. By using Newtons iterative method, this system is solved and the solution of the fractional nonlinear Fredholm integro-differential equations is achieved. Thresholding parameter is used to increase the sparsity of matrix coefficients and the speed of computations. Finally, the method is demonstrated by examples, and then compared results with CAS wavelet method show that our proposed method is more effective and accurate.

Shabnam Paseban Hag

Elnaz Osgooei

Elmira Ashpazzadeh

Alpert wavelet system for solving fractional nonlinear Fredholm integro-differential equations

用于求解分数阶非线性Fredholm积分微分方程的Alpert小波系统

Here, we consider a fourth-order elliptic problem involving singularity and p(x)- biharmonic operator. Using Hardy’s inequality, S+-condition, and Palais-Smale condition, the existence of weak solutions in a bounded domain in RN is proved. Finally, we percent some examples.

Reza Mahdavi Khanghahi

Abdolrahman Razani

Multiple solutions for a fourth-order elliptic equation involving singularity

四阶椭圆方程涉及奇异性的多重解

‎The present study aims are to analyze a delay tumor-immune fractional-order system to describe the rivalry among the immune system and tumor cells. Given that the dynamics of this system depend on the time delay parameter, we examine the impact of time delay on this system to attain better compatibility with actuality. For this purpose, we analytically evaluated the stability of the system’s equilibrium points. It is shown that Hopf bifurcation occurs in the fractional system when the delay parameter passes a certain value. Finally, by using numerical simulations, the analytical results were compared to the numerical results to acquire several dynamical behaviors of this system.

Javad Alidousti

Elham Ghafari

Stability and bifurcation of fractional tumor-immune model with time delay

分数阶肿瘤免疫模型稳定性与时滞分岔

The object of this paper devotes on offering an indirect schemebased on time-fractional Bernoulli functions in the sense ofRieman-Liouville fractional derivative which ends up to the highcredit of the obtained approximate fractional Bessel solutions. Inthis paper, the operational matrices of fractional Rieman-Liouvilleintegration for Bernoulli polynomials are introduced. Utilizingthese operational matrices along with the properties of Bernoullipolynomials and the least squares method, the fractional Besseldifferential equation converts into a nonlinear system of algebraic.To solve these nonlinear algebraic equations which are a prominentproblem, there is a need to employ Newton's iterative method. Inorder to elaborate the study, the synergy of the proposed method isinvestigated and then the accuracy and the efficiency of the methodare clearly evaluated by presenting numerical results

Mohammad Jahangiri Rad

Saber Tavan

Ali Salimi Shamloo

Yaghoub Mahmoudi

A Numerical Scheme for Solving Time-Fractional Bessel Differential Equations

求解时间分数阶贝塞尔微分方程的数值方法

In the present paper, a modified simple equation method is used to obtain exact solutions of the equal width wave Burgers and modified equal width wave Burgers equations. By giving specific values to the parameters, particular solutions are obtained and the plots of solutions are drawn. It shows that the proposed method can be easily generalized to solve a variety of non-linear equations by implementing a robust and straightforward algorithm without the need for any tools.

Azadeh Badiepour

Zainab Ayati

Hamideh Ebrahimi

Obtaining soliton solutions of equations combined with the Burgers and equal width wave equations using a novel method

利用一种新方法求解Burgers方程与等宽波方程组合的孤子解

In this paper, we discuss on the new generalized fractional operator. This operator similarly conformable derivative satisfies properties such as the sum, product/quotient and chain rule. Laplace transform is defined in this case, and some of its properties are stated. In the following, the Sturm-Liouville problems are investigated, and also eigenvalues and eigenfunctions are obtained.

Mohammad Jafari

Farhad Dastmalchi Saei

Ali Asghar Jodayree Akbarfam

The Generalized Conformable Derivative for 4$alpha$-Order Sturm-Liouville Problems

广义顺从导数在4$alpha$阶Sturm-Liouville问题中的应用

In the paper an oscillatory system with liquid dampers is considered, when the mass of the head is large enough. By means of expedient transformations, the equation of motion with fractional derivatives is reduced to an equation of fractional order containing a small parameter. The corresponding nonlocal boundary value problem is solved and the zero and first approximations of solutions of the relative small parameter are constructed. The results are illustrated on the concrete example, where the solution differs from the analytical solution by 10^-2 order.

Fikret Ahmadali Aliev

Nihan Aliev

Nazile Hajiyeva

Nargiz Safarova

Rufana Aliyeva

Asymptotic method for solution of oscillatory fractional derivative

振荡分数阶导数解的渐近方法

In this study, one explicit and one implicit finite differencescheme is introduced for the numerical solution of time-fractionalRiesz space diffusion equation. The time derivative is approximatedby the standard Gr{u}nwald Letnikov formula of order one, whilethe Riesz space derivative is discretized by Fourier transform-basedalgorithm of order four. The stability and convergence of theproposed methods are studied. It is proved that the implicit schemeis unconditionally stable, while the explicit scheme is stableconditionally. Some examples are solved to illustrate the efficiencyand accuracy of the proposed methods. Numerical results confirm thatthe accuracy of present schemes is of order one.

Zeynab Abdollahy

Mahdi Baghmisheh

Two explicit and implicit finite difference schemes for time fractional Riesz space diffusion equation

时间分数阶Riesz空间扩散方程的两种显式和隐式有限差分格式

Abbreviation
Journal Impact	1.12
Quartiles(Global)	MATHEMATICS, APPLIED(Q2)

ISSN	2345-3982, 2383-2533
h-index	10

Publication Information	Publisher: University of Tabriz，Publishing cycle: ，Journal Type: journal，Open Access Journals: Yes
Basic data	Year of publication: 2019，Proportion of original research papers: 100.00%，Self Citation Rate:18.20%， Gold OA Rate: 0.00%
Average review cycle	网友分享经验：4 Weeks

Computational Methods for Differential Equations

Journal Citation Format

A journal article with 1 author

A journal article with 2 authors

A journal article with 3 authors

A journal article with 5 or more authors

Books Citation Format

Thesis Citation Format

Web sites Citation Format

Patent Citation Format

Staying up late manually editing references? ivySCI automatically matches journals and helps you generate references with a single click.

Share Submission Experience