Article
Mathematics, Interdisciplinary Applications
Mati Ur Rahman, Ali Althobaiti, Muhammad Bilal Riaz, Fuad S. Al-Duais
Summary: This article explores a biological population model using a specific numerical method. The numerical simulations reveal a relationship between the population density and the fractional order, showing that a higher fractional order leads to a higher population density. The results demonstrate that the method is suitable and highly accurate in terms of computational cost.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics, Applied
Mohammad Alaroud, Osama Ababneh, Nedal Tahat, Shrideh Al-Omari
Summary: Constructing mathematical models of fractional order and developing numeric-analytic solutions are significant subjects in physics, applied mathematics, and engineering. This study introduces a novel analytical technique called the Laplace residual power series (LRPS) technique to produce approximate solutions for a non-linear time-fractional gas dynamics equation. The technique combines the RPS approach with the Laplace transform operator and has been successfully applied to handle time-FGDE models, generating accurate solutions with fewer computations. The impact of the fractional order on the solutions is also investigated.
Article
Mathematics, Applied
Jagdev Singh, Arpita Gupta
Summary: The main aim of this study is to examine the outcomes of the nonlinear partial modified Degasperis-Procesi equation of arbitrary order using two analytical methods. These methods are based on homotopy and a novel adjustment with the generalized Laplace transform operator. The results show that the fractional order modified Degasperis-Procesi equation is capable of accurately describing the nonlinear aspects of dispersive waves.
Article
Mathematics, Applied
Aisha Abdullah Alderremy, Mahmoud Jafari Shah Belaghi, Khaled Mohammed Saad, Tofigh Allahviranloo, Ali Ahmadian, Shaban Aly, Soheil Salahshour
Summary: This paper introduces a novel q-fractional derivative in the Caputo sense, including a proportional derivative. By applying the q-Laplace transform, solutions to the system are obtained, with the bivariate Mittag-Leffler function playing a key role. The concept is illustrated through two detailed examples.
Article
Materials Science, Multidisciplinary
Ndolane Sene
Summary: This paper considers a specific fluid model and describes its constructive equations using the Caputo derivative. The exact solutions are proposed using the Laplace transformation, and the impacts of various parameters on the modeling are explained in terms of physical viewpoints.
RESULTS IN PHYSICS
(2022)
Article
Multidisciplinary Sciences
Abdulrahman B. M. Alzahrani
Summary: This paper proposes two efficient methods, the Laplace residual power series method and a new iterative method, for solving the fractional-order Schrodinger-KdV system. Numerical experiments show that both methods can produce highly accurate solutions, but the new iterative method is more efficient in terms of computational time and memory usage.
Article
Thermodynamics
Haiyan Zhang, Muhammad Nadeem, Asim Rauf, Zhao Guo Hui
Summary: This paper suggests a novel approach for solving time-fractional differential equations, which does not require any assumptions or hypotheses and is proved to be simple and effective. The proposed method demonstrates originality in directly addressing fractional partial differential equations without the need for any assumptions.
INTERNATIONAL JOURNAL OF NUMERICAL METHODS FOR HEAT & FLUID FLOW
(2021)
Article
Mathematics, Applied
K. R. Madhura, Babitha Atiwali, S. S. Iyengar
Summary: Nanofluids with fractional derivative models and different base fluids and nanoparticle shapes were studied for their memory effect and convective flow, heat, and mass transfer characteristics. The governing equations were solved using Laplace transform technique and the results showed that nanofluids with water-based blade-shaped nanoparticles exhibited enhanced velocity and temperature distributions.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Interdisciplinary Applications
Ridhwan Reyaz, Ahmad Qushairi Mohamad, Yeou Jiann Lim, Muhammad Saqib, Sharidan Shafie
Summary: Fractional derivatives have wide applications in engineering, medical, and manufacturing sciences, and their geometrical representations in fluid flow are still being explored. This study presents an analytical solution to investigate the impact of the Caputo-Fabrizio fractional derivative on magnethohydrodynamic fluid flow with thermal radiation and chemical reaction, and numerical analysis of skin friction, Nusselt number, and Sherwood number.
FRACTAL AND FRACTIONAL
(2022)
Article
Materials Science, Multidisciplinary
Lanre Akinyemi, Kottakkaran Sooppy Nisar, C. Ahamed Saleel, Hadi Rezazadeh, Pundikala Veeresha, Mostafa M. A. Khater, Mustafa Inc
Summary: This study aims to find solutions for the fractional model of the fifth-order weakly nonlocal Schrodinger equation incorporating nonlinearity of the parabolic law and external potential using the q-homotopy analysis transform method. The method provides approximate and exact solutions such as bright soliton, dark soliton, and exponential solutions, showing that only a few terms are needed to achieve precise and reliable results. The results demonstrate the competitive and powerful nature of the projected method for studying complex nonlinear models of fractional type.
RESULTS IN PHYSICS
(2021)
Article
Mathematics, Interdisciplinary Applications
Jun-Sheng Duan, Yu-Jie Lan, Ming Li
Summary: This passage mainly compares the applications of the Weyl fractional derivative and the Caputo fractional derivative in the fractional oscillator equation. Under the two perspectives, the equation has different solutions and response modes. One of the characteristics of the fractional case is the presence of a monotone recovery term in negative power law.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics, Applied
Shujuan An, Kai Tian, Zhaodong Ding, Yongjun Jian
Summary: This study investigates the unsteady electroosmotic slip flow of viscoelastic fluid through a parallel plate microchannel under the combined effect of electroosmotic and pressure gradient forcings. Analytical and numerical methods are used to analyze the velocity and potential distributions. The results show that the time required to reach a steady state is influenced by the fractional calculus parameter alpha, slip coefficient L, Deborah number De, and the ratio of pressure to electroosmotic driving forces. The steady flow rate depends on the slip coefficient L and the normalized electrokinetic width K, and is independent of alpha and De.
APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Engineering, Multidisciplinary
Kashif Ali Abro, Ilyas Khan, Kottakkaran Sooppy Nisar, Abdon Atangana
Summary: This paper proposes the mathematical modeling of electrochemical double layer capacitors and derives the governing equations and transfer functions through fractional differential operators. The results suggest that electrochemical double layer capacitors have higher energy storage capacities and stability compared to conventional capacitors.
ALEXANDRIA ENGINEERING JOURNAL
(2021)
Article
Mathematics, Interdisciplinary Applications
Najma Ahmed, Nehad Ali Shah, Somaye Taherifar, F. D. Zaman
Summary: This article studies the fractional models of cancer tumors using Laplace transform and numerical inversion, highlighting the impact of fractional parameters on tumor cell concentration. The models based on time-fractional derivatives provide a better description of tumor evolution, considering the historical influence of tumor cell concentration on time evolution.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Multidisciplinary Sciences
Muhammad Naeem, Ahmed M. Zidan, Kamsing Nonlaopon, Muhammad I. Syam, Zeyad Al-Zhour, Rasool Shah
Summary: The study uses the new iterative transform method and homotopy perturbation transform method to solve fractional-order Equal-Width equations with Caputo-Fabrizio, providing approximate results in a series form for easy computation. These techniques are reliable, effective, and efficient in studying the nonlinear behavior of plasma systems and highlighting critical points.
Article
Computer Science, Interdisciplinary Applications
Azhar Iqbal, Nur Nadiah Abd Hamid, Ahmad Izani Md Ismail
MATHEMATICS AND COMPUTERS IN SIMULATION
(2020)
Article
Mathematics, Applied
Muhammad Asim Khan, Norhashidah Hj. Mohd Ali, Nur Nadiah Abd Hamid
ADVANCES IN DIFFERENCE EQUATIONS
(2020)
Article
Computer Science, Interdisciplinary Applications
Azhar Iqbal, Nur Nadiah Abd Hamid, Ahmad Izani Md. Ismail, Muhammad Abbas
Summary: This article describes the Galerkin method based on quintic B-spline functions for numerically solving the second order coupled nonlinear Schrodinger equations. Finite difference and Crank-Nicolson schemes were utilized for discretization, comparing numerical results for accuracy and capability assessment. The study shows that using higher order B-spline functions leads to accurate and reliable results.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2021)
Article
Engineering, Multidisciplinary
Muhammad Asim Khan, Norhashidah Hj. Mohd Ali, Nur Nadiah Abd Hamid
Summary: This article introduces a new high-order explicit group iterative scheme for solving the two-dimensional time fractional cable equation, showing stability and convergence with numerical examples to demonstrate accuracy and efficiency.
ALEXANDRIA ENGINEERING JOURNAL
(2021)
Article
Mathematics, Applied
Fouad Mohammad Salama, Nur Nadiah Abd Hamid, Norhashidah Hj Mohd Ali, Umair Ali
Summary: This paper presents a new modified hybrid explicit group (MHEG) iterative method for the efficient and accurate numerical solution of a time-fractional diffusion equation in two space dimensions. The method uses a Laplace transformation in the temporal domain and a new finite difference scheme based on grouping strategy in the spatial discretization. The uniqueness, unconditional stability, and convergence of the method are thoroughly proved using matrix analysis. The numerical results compared to analytical and other approximate solutions demonstrate the viability and efficiency of the proposed algorithm.
Article
Multidisciplinary Sciences
Muhammad Asim Khan, Norma Alias, Ilyas Khan, Fouad Mohammad Salama, Sayed M. Eldin
Summary: In this article, a new higher-order implicit finite difference iterative scheme (FDIS) is developed for solving the two dimension (2-D) time fractional Cable equation (FCE). The proposed FDIS discretizes the time fractional and space derivatives using the Caputo fractional derivative and fourth-order implicit scheme, respectively. Furthermore, the theoretical analysis (convergence and stability) of the proposed scheme is also discussed using the Fourier analysis method. Finally, numerical test problems are presented to demonstrate the effectiveness of the proposed method.
SCIENTIFIC REPORTS
(2023)
Article
Mathematics, Applied
Fouad Mohammad Salama, Alla Tareq Balasim, Umair Ali, Muhammad Asim Khan
Summary: The time-fractional advection-diffusion reaction equation (TFADRE) is widely used in various processes and a key challenge is the design of efficient computational schemes. In this paper, a modified fractional explicit group method (MFEGM) is proposed for solving the two-dimensional TFADRE. The stability and convergence of the method are theoretically proved and numerically affirmed, and the computational efficiency is demonstrated through numerical examples comparing it to the Crank-Nicolson finite difference method (CNFDM).
COMPUTATIONAL & APPLIED MATHEMATICS
(2023)
Article
Physics, Multidisciplinary
Umair Ali, Muhammad Naeem, Abdul Hamid Ganie, Dowlath Fathima, Fouad Mohammad Salama, Farah Aini Abdullah
Summary: This study investigates the fractional order cable model (FCM) using the Riemann-Liouville fractional derivatives (R-LFD). A modified implicit finite difference approximation is employed to numerically solve the FCM. The theoretical analysis of the proposed scheme, including stability and convergence, is conducted using the Fourier series approach. The results show that the scheme is unconditionally stable and the approximate solution converges to the exact solution. A numerical example is provided to demonstrate the application and feasibility of the proposed approach.
FRONTIERS IN PHYSICS
(2023)
Article
Mathematics, Applied
Fouad Mohammad Salama, Nur Nadiah Abd Hamid, Umair Ali, Norhashidah Hj Mohd Ali
Summary: This article proposes the hybrid explicit group (HECi) method and the modified hybrid explicit group (MHEG) method to solve the 2D advection-diffusion problem involving fractional-order derivative of Caputo-type. These methods are able to reduce the computational burden resulting from the nonlocality of fractional-order differential operator. The experimental results show the improved performance of the proposed methods in terms of CPU time, iterations number, and computational cost.
Article
Mathematics
Fouad Mohammad Salama, Norhashidah Hj Mohd Ali, Nur Nadiah Abd Hamid
Summary: An efficient hybrid method is proposed to solve two-dimensional time fractional diffusion equation, with computational cost and memory complexity of O(N) and O(M) respectively. The method is based on Laplace transform method and finite difference scheme, and its stability and convergence are rigorously analyzed using Fourier method. Comparative studies from numerical experiments demonstrate that the hybrid method is accurate and effectively reduces computational cost, memory requirement, and CPU time compared to a standard finite difference scheme.
JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE-JMCS
(2021)
Article
Engineering, Multidisciplinary
Fouad Mohammad Salama, Norhashidah Hj Mohd Ali
INTERNATIONAL JOURNAL OF MATHEMATICAL ENGINEERING AND MANAGEMENT SCIENCES
(2020)
