检索结果-南通市图书馆

New Computation of Unified Bounds via a More General Fractional Operator Using Generalized mittag-leffler function in the Kernel

在线全文

学校读者我要写书评

暂无评论

Computer Modeling in Engineering & Sciences 2021年第1期126卷 359-378页

作者： Saima Rashid Zakia Hammouch Rehana Ashraf Yu-Ming Chu Department of Mathematics Government College UniversityFaisalabadPakistan Division of Applied mathematics Thu Dau Mot UniversityThu Dau Mot CityVietnam Department of Mathematics Lahore CollegeWomen UniversityJhangh CampusLahorePakistan Department of Mathematics Huzhou UniversityHuzhouChina

In the present case,we propose the novel generalized fractional integral operator describing mittag-leffler function in their kernel with respect to another function Φ.The proposed technique is to use graceful amalgamations of the Riemann-Liouville(RL)fractional integral operator and several other fractional ***,several generalizations are considered in order to demonstrate the novel variants involving a family of positive functions n(n∈N)for the proposed fractional *** order to confirm and demonstrate the proficiency of the characterized strategy,we analyze existing fractional integral operators in terms of classical fractional ***,some special cases are apprehended and the new outcomes are also *** obtained consequences illuminate that future research is easy to implement,profoundly efficient,viable,and exceptionally precise in its investigation of the behavior of non-linear differential equations of fractional order that emerge in the associated areas of science and engineering.

关键词： Integral inequality generalized fractional integral with respect to another function increasing and decreasing functions mittag-leffler function

Green function of Generalized Time Fractional Diffusion Equation Using Addition Formula of mittag-leffler function

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Journal of Applied Mathematics and Physics 2022年第9期10卷 2720-2732页

作者： Fang Wang Jinmeng Zhang School of Mathematics and Statistics Changsha University of Science and Technology Changsha China

In this paper, we use the mittag-leffler addition formula to solve the Green function of generalized time fractional diffusion equation in the whole plane and prove the convergence of the Green function.

关键词： mittag-leffler function Mellin Transforms Generalized Time Fractional Diffusion Equation Green function Addition Formula

SIRS epidemic modeling using fractional-ordered differential equations:Role of fear effect

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

International Journal of Biomathematics 2024年第5期17卷 79-100页

作者： Shiv Mangal O.P.Misra Joydip Dhar School of Mathematics and Allied Sciences Jiwaji University GwaliorMadhya PradeshIndia Department of Mathematics Post Graduate College BinaMadhya PradeshIndia Department of Applied Sciences Atal Bihari Vajpayee-Indian Institute of Information Technology and Management GwaliorMadhya PradeshIndia

In this paper,an SIRS epidemic model using Grunwald-Letnikov fractional-order derivative is formulated with the help of a nonlinear system of fractional differential equations to analyze the effects of fear in the population during the outbreak of deadly infectious *** criteria for the spread or extinction of the disease are derived and discussed on the basis of the basic reproduction *** condition for the existence of Hopf bifurcation is discussed considering fractional order as a bifurcation ***,using the Grunwald-Letnikov approximation,the simulation is carried out to confirm the validity of analytic results *** the real data of COVID-19 in India recorded during the second wave from 15 May 2021 to 15 December 2021,we estimate the model parameters and find that the fractional-order model gives the closer forecast of the disease than the classical *** the analytical results and numerical simulations presented in this study suggest different policies for controlling or eradicating many infectious diseases.

关键词： SIRS epidemic model fear effect mittag-leffler function Hopf bifurcation parameter estimation

Analytical solution for the time-fractional heat conduction equation in spherical coordinate system by the method of variable separation

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Acta Mechanica Sinica 2011年第6期27卷 994-1000页

作者： Ting-Hui Ning Xiao-Yun Jiang School of Mathematics Shandong University 250100 Jinan China

In this paper,using the fractional Fourier law,we obtain the fractional heat conduction equation with a time-fractional derivative in the spherical coordinate *** method of variable separation is used to solve the timefractional heat conduction *** Caputo fractional derivative of the order 0 〈 α≤ 1 is *** solution is presented in terms of the mittag-leffler *** results are illustrated graphically for various values of fractional derivative.

关键词： Fractional Fourier law Fractional heat conduction equation - Spherical coordinate system - The separation of variables mittag-leffler function

Analytical Approach for Nonlinear Partial Differential Equations of Fractional Order

在线全文

学校读者我要写书评

暂无评论

Communications in Theoretical Physics 2013年第9期60卷 269-277页

作者： Pradip Roul Visvesvaraya National Institute of Technology Department of Mathematics

The purpose of the paper is to present analytical and numerical solutions of a degenerate parabolic equation with time-fractional derivatives arising in the spatial diffusion of biological populations. The homotopy-perturbation method is employed for solving this class of equations, and the time-fractional derivatives are described in the sense of Caputo. Comparisons are made with those derived by Adomian＇s decomposition method, revealing that the homotopy perturbation method is more accurate and convenient than the Adomian＇s decomposition method. Furthermore, the results reveal that the approximate solution continuously depends on the time-fractional derivative and the proposed method incorporating the Caputo derivatives is a powerful and efficient technique for solving the fractional differential equations without requiring linearization or restrictive assumptions. The basis ideas presented in the paper can be further applied to solve other similar fractional partial differential equations.

关键词： reaction-diffusion equation fractional calculus Homotopy-perturbation method biological pop-ulation model mittag-leffler function

A Generalization of the Concept of q-fractional Integrals

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Sinica,English Series 2009年第10期25卷 1635-1646页

作者： Predrag M.RAJKOVIC Sladjana D.MARINKOVIC Miomir S.STANKOVIC Faculty of Mechanical Engineering University of Nis Faculty of Electronic Engineering University of Nis Faculty of Occupational Safety University of Nis

In this paper, we consider the fractional q-integral with variable lower limit of integration. We prove the semigroup property of these integrals, and a formula of Leibniz type. Finally, we evaluate fractional q-integrals of some functions. The consideration of q-exponential function in that sense leads to q-analogs of mittag-Leffier function.

关键词： basic hypergeometric functions q-integral q-derivative fractional integrals mittag-leffler function

On the partial stability of nonlinear impulsive Caputo fractional systems

在线全文

学校读者我要写书评

暂无评论

Applied Mathematics(A Journal of Chinese Universities) 2023年第2期38卷 166-179页

作者： Boulbaba Ghanmi Saifeddine Ghnimi Department of Mathematics Faculty of SciencesUniversity of GafsaTunisia

In this work,stability with respect to part of the variables of nonlinear impulsive Caputo fractional differential equations is *** effective sufficient conditions of stability,uniform stability,asymptotic uniform stability and mittag leffler *** approach presented is based on the specially introduced piecewise continuous Lyapunov ***,some numerical examples are given to show the effectiveness of our obtained theoretical results.

关键词： impulsive fractional differential equations mittag-leffler function partial stability Caputo derivative

New Exact Solutions of Fractional Zakharov–Kuznetsov and Modified Zakharov–Kuznetsov Equations Using Fractional Sub-Equation Method

在线全文

学校读者我要写书评

暂无评论

Communications in Theoretical Physics 2015年第1期63卷 25-30页

作者： S.Saha Ray S.Sahoo Department of Mathematics National Institute of Technology Rourkela Orissa- 769008 India

In the present paper, we construct the analytical exact solutions of some nonlinear evolution equations in mathematical physics; namely the space-time fractional Zakharov–Kuznetsov(ZK) and modified Zakharov–Kuznetsov(m ZK) equations by using fractional sub-equation method. As a result, new types of exact analytical solutions are obtained. The obtained results are shown graphically. Here the fractional derivative is described in the Jumarie's modified Riemann–Liouville sense.

关键词： fractional sub-equation method space-time fractional Zakharov-Kuznetsov (ZK) equation space-time fractional modified Zakharov-Kuznetsov (mZK) equation modified Riemann-Liouvillederivative mittag-leffler function

GENERALIZED FRACTIONAL CALCULUS OF THE ALEPH-function INVOLVING A GENERAL CLASS OF POLYNOMIALS

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Scientia 2015年第5期35卷 1095-1110页

作者： R.K.SAXENA D.KUMAR Department of Mathematics and Statistics Jai Narain Vyas University

The object of this article is to study and develop the generalized fractional calcu- lus operators given by Saigo and Maeda in 1996. We establish generalized fractional calculus formulas involving the product of R-function, Appell function F3 and a general class of poly- nomials. The results obtained provide unification and extension of the results given by Saxena et al. [13], Srivastava and Grag [17], Srivastava et al. [20], and etc. The results are obtained in compact form and are useful in preparing some tables of operators of fractional calculus. On account of the general nature of the Saigo-Maeda operators, R-function, and a general class of polynomials a large number of new and known results involving Saigo fractional calculus operators and several special functions notably H-function, /-function, mittag-Leffier function, generalized Wright hypergeometric function, generalized Bessel-Maitland function follow as special cases of our main findings.

关键词： generalized fractional calculus operators a general class of polynomials R-function H-function /-function generalized Wright hypergeometric function mittag-leffler function generalized Bessel-Maitland function