相关参考文献
注意:仅列出部分参考文献,下载原文获取全部文献信息。
Article
Engineering, Marine
Nazek A. Obeidat et al.
Summary: In this research work, the existence and uniqueness of solution for a novel method called tempered fractional natural transforms (TFNT) are presented and error estimates are given. This efficient method is applied to models, such as the time-space tempered fractional convection-diffusion equation (FCDE) and tempered fractional Black-Scholes equation (FBSE). Exact solutions for these models are obtained using the proposed methodology, which is important for understanding wave behavior in ocean engineering models and related studies in marine science and engineering.
JOURNAL OF OCEAN ENGINEERING AND SCIENCE
(2023)
Article
Mathematics, Applied
Gulalai et al.
Summary: The focus of this manuscript is to analyze the new nonlinear time-fractional (2+1)-dimensional modified KdV equation involving the Atangana-Baleanu Caputo (ABC) derivative. The Laplace Adomian decomposition method (LADM) is applied to extract a semi-analytical solution, and the fixed point theory is used to derive results regarding the existence and uniqueness of solutions. Graphical representations confirm that the ABC operator produces better dynamics, and a comparison between different operators shows that the ABC operator outperforms the Caputo-Fabrizio operator.
Article
Mathematics, Interdisciplinary Applications
Zareen A. Khan et al.
Summary: In this paper, the dynamics of an infectious disease model with imperfect testing and diagnostics is studied using a new fractional order operator. Fixed point theorems are used to verify the existence of the model, and Picard's stability technique is employed to analyze the stability. Numerical computations are also conducted to illustrate the results graphically.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2022)
Article
Mathematics, Applied
Zareen A. Khan et al.
Summary: Four-dimensional continuous chaotic models with Caputo fractional derivative are presented. Fixed point theory is used to investigate the existence and uniqueness of complex systems. The dynamical properties, including the Lyapunov exponent, phase portrait, and time series analysis, are studied. The hyperchaotic nature of each system is revealed by the positive exponents. The numerical method is introduced to describe the influence of the order of the Caputo fractional derivative. The phase portraits are presented to investigate the behavior and effect of some key parameters and fractional orders on model dynamics.
JOURNAL OF FUNCTION SPACES
(2022)
Article
Mathematics
Haifa Bin Jebreen et al.
Summary: This paper introduces the wavelet Galerkin method to solve the Fractional Riccati equation. By introducing biorthogonal Hermite cubic Spline scaling bases and representing the fractional integral as an operational matrix, the integral equation is simplified to a system of algebraic equations. The unknown solution is obtained by solving this system using Newton's iterative method, and the convergence analysis demonstrates the effectiveness and accuracy of the method.
Article
Physics, Multidisciplinary
S. Y. Lou et al.
Summary: This letter discusses the possibility of linear superpositions in nonlinear systems and shows that balancing different nonlinear effects can lead to non-trivial solutions.
Article
Mathematics, Applied
Rongfang Wu et al.
Summary: In this paper, we propose a conforming finite element method for shallow shell and clamped plate models. The first two displacement components are approximated using conforming linear elements, while the third displacement component is approximated using a conforming Hsieh-Clough-Tocher element. We rigorously deduce a convergent theorem independent of mesh steps and validate the theoretical results through numerical experiments.
APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Mathematics, Applied
Shabir Ahmad et al.
Summary: This paper discusses the importance of finding the exact solution to nonlinear PDEs of non-integer orders. It proposes the Yang transform homotopy perturbation technique and presents the relation between the Yang transform and Laplace transform. The paper deduces a procedure for computing the solution of fractional-order nonlinear PDEs and shows the convergence and error estimate of the suggested method. Examples are provided to illustrate the novel method, and a comparison between the approximate and exact solutions is given.
Article
Mathematics, Applied
Shabir Ahmad et al.
Summary: In this article, the HIV-1 infection mathematical model is generalized using a nonsingular fractional operator. The existence and stability of a unique solution to the model under the suggested operator are addressed using Picard-Lindelof and fixed-point theory. Numerical simulations are provided to study the complex dynamics of the model for different fractional orders.
Article
Engineering, Multidisciplinary
Sayed Saifullah et al.
Summary: In this article, the time-fractional nonlinear Klein-Gordon equation is studied using Caputo-Fabrizio's and Atangana-Baleanu-Caputo's operators. Solutions are obtained using the modified double Laplace transform decomposition method, showing convergence to the exact solution. Numerical solutions demonstrate the existence of pulse-shaped solitons in the considered model.
MATHEMATICAL PROBLEMS IN ENGINEERING
(2021)
Article
Materials Science, Multidisciplinary
Aziz Khan et al.
Summary: This article investigates the existence of results and stability analysis for a nabla discrete ABC-fractional order COVID-19 model, and provides an illustrative example for its application. The study finds that the nabla discrete ABC-fractional operator is more general and applicable in modeling dynamical problems, although certain conditions are needed to ensure the proofs of existence and uniqueness theorems, as well as Hyers-Ulam stability.
RESULTS IN PHYSICS
(2021)
Article
Mathematics
Naveed Iqbal et al.
Summary: In this article, a technique combining the Elzaki transformation and the new iteration technique is developed to determine the analytical result of certain Kaup-Kupershmidt equations. This approach proves to be effective and suitable for applying in similar nonlinear problems, serving as an alternative method to existing approaches for accurate models.
JOURNAL OF MATHEMATICS
(2021)
Article
Physics, Multidisciplinary
Ravi P. Agarwal et al.
Summary: This research article explores the solution of fractional-order parabolic equations using the Adomian decomposition method and natural transform, providing simple and attractive closed form solutions. The obtained results are found to be in good agreement with exact solutions, with convergence observed between fractional and integer-order problem solutions. The technique is considered accurate and can be applied to solve other fractional-order partial differential equations.
Article
Engineering, Multidisciplinary
Amita Devi et al.
Summary: This article discusses fractional Langevin equations with Caputo Hadamard-derivative, involving non-local integral and non-periodic boundary conditions. The stability, existence, and uniqueness of solutions are defined using the Krasnoselskii fixed point theorem and the Banach contraction mapping principle. An application is provided to facilitate the understanding of the hypothetical outcomes.
ALEXANDRIA ENGINEERING JOURNAL
(2021)
Article
Mathematics, Applied
Sajjad Ali Khan et al.
Summary: The study focuses on analyzing a Hepatitis B model under the Caputo-Fabrizio fractional derivative, utilizing qualitative and semi-analytical methods. Results are obtained using fixed point theory and decomposition method, and the dynamics of different compartments in the model are presented through graphs.
Article
Engineering, Multidisciplinary
Kamal Shah et al.
ALEXANDRIA ENGINEERING JOURNAL
(2020)
Proceedings Paper
Mathematics, Applied
Tayyaba Akram et al.
PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES AND TECHNOLOGY 2018 (MATHTECH 2018): INNOVATIVE TECHNOLOGIES FOR MATHEMATICS & MATHEMATICS FOR TECHNOLOGICAL INNOVATION
(2019)
Article
Mathematics, Applied
Rodrigue Gnitchogna et al.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2018)
Article
Engineering, Mechanical
S. Saha Ray et al.
JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS
(2016)