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Article
Mathematics, Applied
Adel Abd Elaziz El-Sayed et al.
Summary: This article presents a numerical technique for solving the fractional-order logistic equation using the operational matrices of the Dickson polynomials. The technique transforms the problem into a system of matrices, solves it using appropriate numerical techniques, and discusses its convergence and error estimate. Numerical applications demonstrate the applicability, accuracy, and efficiency of the technique, and compare the results with previous methods to show its advantages.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Computer Science, Artificial Intelligence
Jia-Li Wei et al.
Summary: This paper proposes a multi-layer neural network for deep learning based on fractional differential equations, and uses parallel computing to search for an optimal structure. The Caputo derivative is approximated by L1 numerical scheme, and an unconstrained discretization minimization problem is presented. The efficiency of the method is demonstrated through analytical approximate solutions of two fractional logistic equations (FLEs). Furthermore, the fractional order and other parameters of FLEs are estimated using the gradient descent algorithm, and the proposed optimal NN method is used for forecasting. Comparative studies show that FLEs have more parameter freedom degrees and outperform the classical logistic model.
NEURAL COMPUTING & APPLICATIONS
(2023)
Article
Mathematics, Applied
Pooja Yadav et al.
Summary: The research aims to find approximate solutions to second-order Fredholm integral problems using the Fibonacci Wavelet. The Fibonacci wavelet collocation technique is used to approximate the problem. By transforming the Fredholm integral equations into algebraic equations with unknown Fibonacci coefficients, the convergence analysis and error estimation of the Fibonacci wavelet are briefly discussed. The results obtained from this methodology are presented through tables and graphs, and are compared with Hermite cubic spline to demonstrate the novelty and precision of the suggested numerical approach.
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS
(2023)
Article
Mathematics, Applied
Anh Tuan Nguyen et al.
Summary: This paper investigates a modified version of the Keller-Segel model. The classical derivative with respect to time is replaced by the time-fractional derivative in the sense of Caputo to consider memory effects on the model. The well-posedness of the Cauchy problem associated with the modified model is focused on. Global solutions are obtained in a critical homogeneous Besov space for the case when the spatial variable is considered in the space R-d and the initial datum is sufficiently small. For the case of bounded domain, the existence and uniqueness of a mild solution in Hilbert scale spaces are provided using a discrete spectrum of the Neumann Laplace operator. The blowup behavior is also studied. To obtain the results, the Banach fixed point theorem and special functions such as the Mainardi function and the Mittag-Leffler function are used.
ADVANCES IN NONLINEAR ANALYSIS
(2023)
Article
Mathematics, Applied
Juan J. Nieto
Summary: We studied the logistic differential equation of fractional order and non-singular kernel, and obtained the analytical solution.
APPLIED MATHEMATICS LETTERS
(2022)
Article
Mathematics, Applied
Laique Zada et al.
Summary: In this study, the Haar wavelet collocation method is applied for the numerical solution of fractional partial differential equations. The proposed method is semi-analytic and has been tested for accuracy, efficiency, and simplicity.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2022)
Article
Mathematics, Applied
Nguyen Huy Tuan et al.
Summary: This article investigates the nonlocal nonlinear reaction-diffusion system with final conditions and proposes a modified quasi-reversibility model to stabilize the ill-posed problem. Numerical results are provided to demonstrate the effectiveness of the method.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2022)
Article
Computer Science, Interdisciplinary Applications
Mo Faheem et al.
Summary: This paper aims to develop an improved Hermite wavelet resolution method for solving space-time-fractional partial differential equations (STFPDE). The proposed method directly formulates the Riemann-Liouville fractional integral (RLFI) operator for Hermite wavelets of general order integration, which enhances the theoretical applicability and computational reliability compared to previous wavelet methods.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2022)
Article
Mathematics, Applied
Juan J. Nieto
Summary: We solve the logistic differential equation for generalized proportional Caputo fractional derivative using a fractional power series solution. The coefficients of the power series are connected to Euler polynomials, Euler numbers, and a recently introduced sequence of Euler's fractional numbers. Numerical approximations are provided to demonstrate the accuracy of truncating the fractional power series. This extends previous studies on the Caputo fractional logistic differential equation and Euler numbers.
FRACTIONAL CALCULUS AND APPLIED ANALYSIS
(2022)
Article
Mathematics, Applied
Weiyi Zhang et al.
Summary: In this paper, we study the fractional parabolic-elliptic Keller-Segel system with a time-space dependent logistic source. We prove the local existence and uniqueness of nonnegative classical solutions, as well as the global existence and boundedness of classical solutions under certain parameter conditions. We also find the pointwise persistence phenomena and uniform persistence phenomena of the solutions.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics, Applied
Nguyen Duc Phuong et al.
Summary: This paper is dedicated to identifying an unknown source for a time-fractional diffusion equation in a general bounded domain. It first proves the non-well posedness of the problem and the stability of the source function. Then, by using the Modified Fractional Landweber method, it presents regularization solutions and demonstrates the convergence rate between regularization solutions and sought solution under different choice rules of the regularization parameter. Finally, an illustrative numerical example is provided to validate the results of the theory.
ACTA MATHEMATICA SINICA-ENGLISH SERIES
(2022)
Article
Mathematics, Applied
Nguyen Huy Tuan et al.
Summary: This work studies two final value problems for the fractional reaction equation with standard Brownian motion and fractional Brownian motion. The well-posedness of each problem is investigated under strong data choices, and a regularization method called Fourier truncation is applied to construct regularized solutions. Convergence results of the regularized solutions are also proposed.
BULLETIN DES SCIENCES MATHEMATIQUES
(2022)
Article
Mathematics, Applied
Nguyen Duc Phuong et al.
Summary: In this paper, we studied a pseudo-parabolic equation with the Atangana-Baleanu Caputo fractional derivative. We used the Fractional Tikhonov method and the generalized Tikhonov method as our main tools and provided numerical experiments to validate our theory.
Article
Acoustics
Sedigheh Sabermahani et al.
Summary: This study introduces a computational method for solving fractional optimal control problems using Fibonacci wavelets, discussing the convergence of the algorithm and demonstrating its effectiveness through numerical examples, while also examining fractional optimal control problems from a bibliometric perspective.
JOURNAL OF VIBRATION AND CONTROL
(2021)
Article
Mathematics, Applied
Ngoc Tran Bao et al.
Summary: This paper studies the well-posedness of the terminal value problem in time-fractional wave equations with Caputo derivative, proving the existence, uniqueness, and continuous dependence of solutions, and obtaining some regularity results for solutions. The effectiveness of the methods are demonstrated by applying the results to two interesting models.
Article
Computer Science, Software Engineering
Mohd Irfan et al.
Summary: In this paper, an efficient wavelet method based on Fibonacci polynomials is developed for solving the Pennes bioheat transfer equation. The technique constructs Fibonacci wavelets using Fibonacci polynomials, applies spectral collocation technique, and uses the Newton method to solve the resulting algebraic equation system. Results show that the proposed technique is effective for solving Pennes bioheat transfer equations and similar types of partial differential equations numerically.
INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING
(2021)
Article
Physics, Multidisciplinary
I Area et al.
Summary: By using a series of fractional powers, a representation of the solution to the fractional logistic equation is presented and proven to be the exact solution in the simplest case. Numerical approximations demonstrate the good approximations obtained by truncating the fractional power series.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2021)
Article
Mathematics
Fernando Alcantara-Lopez et al.
Summary: A new growth model is proposed, incorporating Logistics and Gompertz models and including Caputo-type fractional derivative, with non-fixed inflection point. The model can also describe multiple sigmoidal behaviors and multiple inflection points.
Article
Automation & Control Systems
Sedigheh Sabermahani et al.
OPTIMAL CONTROL APPLICATIONS & METHODS
(2020)
Article
Physics, Multidisciplinary
Liyana Nadhira Kaharuddin et al.
EUROPEAN PHYSICAL JOURNAL PLUS
(2020)
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Mathematics, Applied
Hari M. Srivastava et al.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2020)
Article
Engineering, Multidisciplinary
Nadir Djeddi et al.
ALEXANDRIA ENGINEERING JOURNAL
(2020)
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Mathematics, Interdisciplinary Applications
Efim Pelinovsky et al.
CHAOS SOLITONS & FRACTALS
(2020)
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Mathematics, Interdisciplinary Applications
Valentina V. Tarasova et al.
CHAOS SOLITONS & FRACTALS
(2017)
Article
Mathematical & Computational Biology
Suayip Yuzbasi
INTERNATIONAL JOURNAL OF BIOMATHEMATICS
(2016)
Article
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M. M. Khader
DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS
(2016)
Article
Mathematics, Applied
Mujeeb Ur Rehman et al.
JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY
(2015)
Review
Agriculture, Dairy & Animal Science
H. Darmani Kuhi et al.
WORLDS POULTRY SCIENCE JOURNAL
(2010)
Article
Mathematics, Applied
A. M. A. El-Sayed et al.
APPLIED MATHEMATICS LETTERS
(2007)
Article
Mathematics, Applied
Adem Kilicman et al.
APPLIED MATHEMATICS AND COMPUTATION
(2007)
