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Article
Mathematics, Interdisciplinary Applications
Xuan Liu et al.
Summary: This paper deals with a fractional mathematical model for the spread of polio in a community with variable size structure, considering the role of vaccination. The model is extended using the Atangana-Baleanu method and the Caputo fractional operator. The positivity and boundedness of the solution are presented, and the fixed-point theory is used to study the existence and uniqueness of the solution. The stability of the model is also investigated using the Ulam-Hyers stability scheme. Numerical simulations and control simulations are performed, and various graphical presentations are given to understand the dynamics of the model at different fractional orders.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2022)
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, Applied
Sayed Saifullah et al.
Summary: In this study, the nonlinear Klein-Gordon equation with Caputo fractional derivative is investigated. The general solution of the system is derived using the composition of the double Laplace transform with the decomposition method, and it is shown that the obtained solution converges to the exact solution. The validity and accuracy of the proposed method are demonstrated through specific examples, and good agreements are obtained. The results reveal the existence of soliton solutions in the proposed system, and the amplitude of the wave solution increases with deviations in time.
Article
Physics, Multidisciplinary
Sara Abdelsalam et al.
Summary: This article studies the impact of laser radiation and chemical reaction on hybrid non-Newtonian fluid through a sinusoidal channel. A mathematical model is used to simulate the non-linear partial differential equations and the effect of relevant parameters on the fluid flow and temperature distribution is discussed. The results show that laser radiation enhances the fluid flow and heat transfer, which is significant in disease treatment.
WAVES IN RANDOM AND COMPLEX MEDIA
(2022)
Article
Mathematics, Applied
A. M. Alsharif et al.
Summary: The purpose of this investigation is to theoretically study the effect of unsteady electroosmotic flow (EOF) in an incompressible fractional second-grade fluid with low-density mixtures of two spherical nanoparticles, copper and titanium. Analytical and numerical methods are used to obtain solutions for the velocity and heat equations, and the variations of velocity and heat transfer with respect to different parameters are presented graphically. This research has theoretical implications for biofluid-based microfluidic transport systems.
APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION
(2022)
Article
Mathematical & Computational Biology
Sara Abdelsalam et al.
Summary: The goal of this research is to investigate the effect of electroosmotic forces on the swimming of sperms in the cervical canal. The results show that using a hyperbolic tangent fluid as the base liquid is more appropriate for simulating and discussing the motility of cervical fluid. The motility of mucus velocity is more applicable to the upper swimming sheet of propulsive spermatozoa with small power law index values, and increases with the electroosmotic parameter and Helmholtz-Smoluchowski velocity.
MATHEMATICAL MODELLING OF NATURAL PHENOMENA
(2022)
Article
Mathematics, Interdisciplinary Applications
Mati Ur Rahman et al.
Summary: This article describes the dynamics of a fractional mathematical model of serial killing using the Mittag-Leffler kernel. Through the fixed point theory approach, a qualitative analysis is conducted and a result is established to ensure the existence of at least one solution. Ulam's stability of the model is demonstrated using nonlinear concepts. The iterative fractional-order Adams-Bashforth approach is employed to find an approximate solution. The suggested method is numerically simulated at various fractional orders, and the simulation shows that all compartments achieve convergence and stability over time, with lower fractional orders achieving stability sooner.
FRACTAL AND FRACTIONAL
(2022)
Article
Engineering, Marine
Sania Qureshi et al.
Summary: The study delves into novel mathematical methods using different differential operators for solving RL and RC circuit models, with numerical simulations conducted in MATLAB to reveal new solution behaviors.
JOURNAL OF OCEAN ENGINEERING AND SCIENCE
(2021)
Article
Fazlur Rahman et al.
International Journal of Applied and Computational Mathematics
(2021)
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
Mathematics, Interdisciplinary Applications
Amir Ali et al.
Summary: This study analytically investigates a nonlinear fractional-order sine-Gordon equation using Caputo's derivatives. The Laplace transform combined with the Adomian decomposition method is employed to obtain analytical approximation of the equation, with numerical simulations confirming qualitatively better agreements with the analytical results.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2021)
Article
Mathematics
Sania Qureshi
Summary: This study investigates the second order linear ordinary differential equation mass spring damper system using the Sumudu integral transform and Caputo type differential operator to find a closed form solution. The solution, in terms of the Fox H-function, offers different aspects depending on the values of alpha (in (1,2]) and beta (in (0,1]). The classical mass spring damper model is obtained when alpha = beta = 1.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTATIONAL MECHANICS
(2021)
Article
Mathematics, Applied
M. Erfanian et al.
ADVANCES IN DIFFERENCE EQUATIONS
(2020)
Article
Mathematics, Interdisciplinary Applications
Wangrong Ma et al.
CHAOS SOLITONS & FRACTALS
(2019)
Article
Materials Science, Multidisciplinary
E. A. Yousif et al.
RESULTS IN PHYSICS
(2018)
Article
Thermodynamics
Abdon Atangana et al.
Article
Automation & Control Systems
Montri Thongmoon et al.
NONLINEAR ANALYSIS-HYBRID SYSTEMS
(2010)
Article
Mathematics, Applied
Hassan Eltayeb et al.
APPLIED MATHEMATICS LETTERS
(2008)
Article
Mathematics, Interdisciplinary Applications
Abdul-Majid Wazwaz
CHAOS SOLITONS & FRACTALS
(2008)
Article
Physics, Multidisciplinary
S. Z. Rida et al.
