Article
Mathematics, Interdisciplinary Applications
Javed Khan, Mati Ur Rahman, Muhammad Bilal Riaz, Jan Awrejcewicz
Summary: This paper studies the dynamics of the Dengue disease model using a novel piecewise derivative approach. The existence and uniqueness of a solution with piecewise derivative are examined, and a numerical simulation is conducted. The work clarifies the concept of piecewise derivatives and the dynamics of the crossover problem.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2022)
Article
Mathematics, Applied
Omar Abu Arqub, Jagdev Singh, Mohammed Alhodaly
Summary: This study presents a mathematical modeling approach for uncertain fractional integrodifferentials (FIDEs) in electric circuits, signal processing, electromagnetics, and anomalous diffusion systems. A numerical method based on the reproducing kernel algorithm (RKA) is used to solve groups of fuzzy fractional integrodifferentials (FFIDEs) with Atangana-Baleanu-Caputo (ABC) fractional distributed order derivatives. Experimental results demonstrate the feasibility and accuracy of the proposed approach, indicating its potential for treating various models with fractional ABC distributed order.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Physics, Multidisciplinary
Banan Maayah, Omar Abu Arqub, Salam Alnabulsi, Hamed Alsulami
Summary: This paper discusses a mathematical model that investigates the interaction between IS and CC. By utilizing fractional differential problems and the reproducing Hilbert scheme, the mathematical and physiological behavior of the disease is analyzed, along with the effect of the degree of fractional derivatives used.
CHINESE JOURNAL OF PHYSICS
(2022)
Article
Mathematics, Applied
Mubashara Wali, Sadia Arshad, Sayed M. Eldin, Imran Siddique
Summary: In this study, the approximate solutions for time-space fractional linear and nonlinear diffusion equations are obtained. A finite difference approach is used to solve both linear and nonlinear fractional order diffusion problems. The Riesz fractional derivative in space is approximated using a centered difference scheme. The stability and convergence of the proposed scheme are analyzed, and the results show that the recommended method converges at a rate of O(delta t2 + h2) for mesh size h and time steps delta t. The application of the model is also examined through graphic results and numerical examples.
Article
Computer Science, Theory & Methods
Ho Vu, Behzad Ghanbari, Ngo Van Hoa
Summary: In this paper, the generalized Atangana-Baleanu (GAB) type fractional calculus is introduced as a generalization of Atangana-Baleanu type fractional calculus with respect to the generalized Mittag-Leffler kernel. The existence and uniqueness results for initial value problems of fuzzy differential equations involving a GAB fractional derivative in the Caputo sense are established using the method of successive approximation and fixed point theorems. Some examples and numerical simulations are provided to visualize the theoretical results.
FUZZY SETS AND SYSTEMS
(2022)
Article
Multidisciplinary Sciences
Muhammad Arif, Poom Kumam, Wiyada Kumam, Ali Akgul, Thana Sutthibutpong
Summary: The study investigates the application of fractal-fractional derivatives in the model of couple stress fluid, showing the more general nature of fractal-fractional solutions compared to classical and fractional solutions. Additionally, the fractal-fractional model exhibits better memory effect on the dynamics of couple stress fluid in channel compared to the fractional model of CSF.
SCIENTIFIC REPORTS
(2021)
Article
Mathematics, Applied
Muhammad Farman, Ali Akgul, Sameh Askar, Thongchai Botmart, Aqeel Ahmad, Hijaz Ahmad
Summary: This study proposes a mathematical model for the transmission of the Zika virus through mosquitoes and validates its effectiveness and stability through simulations and calculations. The model is of great importance for future analysis and the development of control strategies for the Zika virus.
Article
Physics, Multidisciplinary
Lalchand Verma, Ramakanta Meher
Summary: This study develops a novel fuzzy fractional model for the human liver and utilizes ABC gH-differentiability and a fuzzy double parametric q-homotopy analysis method. Numerical experiments show that the proposed method is more accurate and superior to the generalized Mittag-Leffler function method, as it coincides with most clinical data.
EUROPEAN PHYSICAL JOURNAL PLUS
(2022)
Article
Mathematics, Interdisciplinary Applications
Kishor D. Kucche, Sagar T. Sutar
Summary: In this paper, estimations on the Atangana-Baleanu-Caputo fractional derivative at extreme points are determined, leading to comparison results. Peano's type existence results for nonlinear fractional differential equations involving Atangana-BaleanuCaputo fractional derivative are established. The acquired comparison results are then used to address the existence of local, extremal, and global solutions.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Materials Science, Multidisciplinary
Mohammad Partohaghighi, Marzieh Mortezaee, Ali Akgul, Sayed M. Eldin
Summary: Transport of contaminants is a crucial environmental issue, and accurate modeling is vital for effective management strategies. This study introduces a non-integer model for the advection-dispersion problem in contaminant transport. The numerical solution is obtained using discrete Chebyshev polynomials and an operational matrix. The suggested scheme is validated through comparison with other numerical methods.
RESULTS IN PHYSICS
(2023)
Article
Materials Science, Multidisciplinary
Badr Saad T. Alkahtani, Ilknur Koca
Summary: In this paper, the applicability of fractional stochastic differential equations in an SIR model was further explored. The analysis and numerical simulations were conducted for different fractional orders and densities of randomness, providing insights into the processes following both randomness and memory nonlocality.
RESULTS IN PHYSICS
(2021)
Article
Mathematics, Applied
Iskander Tlili, Nehad Ali Shah, Saif Ullah, Humera Manzoor
Summary: The study analyzed a one-dimensional generalized fractional advection-diffusion equation with a time-dependent concentration source on the boundary, obtaining an analytical solution using Laplace transform and finite sine-Fourier transform. The impact of memory parameter on solute concentration was investigated, revealing that the solute concentration increases with fractional parameter. The study also found that an advection-diffusion process described by Atangana-Baleanu time-fractional derivative leads to a smaller solute concentration compared to the classical process for a constant concentration source on the boundary.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Multidisciplinary Sciences
Hasan S. Panigoro, Agus Suryanto, Wuryansari Muharini Kusumawinahyu, Isnani Darti
Summary: This paper presents a fractional-order eco-epidemic model based on the Rosenzweig-MacArthur predator-prey model, utilizing Caputo and ABC fractional differential operators to obtain solutions. Numerical simulations show similar dynamics between the two models, with the main difference being the convergence rate to stable equilibrium points.
Article
Mathematics, Applied
Ramazan Ozarslan
Summary: This article examines the use of the two-parameter Weibull model with new fractional differential operators to analyze microbial survival curves, comparing the effects of different fractional derivatives on microbial cell survival and growth rates, and discussing the advantages and disadvantages of different fractional derivatives.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Materials Science, Multidisciplinary
Saima Rashid, Aasma Khalid, Sobia Sultana, Fahd Jarad, Khadijah M. Abualnaja, Y. S. Hamed
Summary: This paper develops and evaluates a mathematical model based on fractional differential equations to capture the mechanisms of oncolytic virotherapy. The study investigates the stability and uniqueness of solutions, and demonstrates that the introduction of fractional derivatives can improve the accuracy of the system.
RESULTS IN PHYSICS
(2022)
Article
Mathematics, Applied
Omar Abu Arqub, Jagdev Singh, Banan Maayah, Mohammed Alhodaly
Summary: In this research study, fuzzy fractional differential equations in presence of the Atangana-Baleanu-Caputo differential operators are analyzed and solved using extended reproducing kernel Hilbert space technique. A new fuzzy characterization theorem and two fuzzy fractional solutions are constructed and computed. The convergence analysis and error behavior beyond the reproducing kernel theory are explored and discussed. Three computational algorithms and modern trends in terms of analytic and numerical solutions are demonstrated. The dynamical characteristics and mechanical features of these fuzzy fractional solutions are illustrated and studied. Highlights and future suggested research work are provided.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Computer Science, Interdisciplinary Applications
Hind Sweis, Omar Abu Arqub, Nabil Shawagfeh
Summary: This paper considers linear and nonlinear fractional delay Volterra integro-differential equations in the ABC sense. The authors used the continuous Laplace transform to find equivalent Volterra integral equations and apply the Arzela-Ascoli theorem and Schauder's fixed point theorem to prove the local existence solution. They also successfully construct and prove the global existence and uniqueness of the solution for the considered fractional delay integro-differential equation using the obtained Volterra integral equations and the contraction mapping theorem. The Galerkin algorithm with shifted Legendre polynomials is used for the approximation procedure.
INTERNATIONAL JOURNAL OF MODERN PHYSICS C
(2023)
Article
Engineering, Multidisciplinary
Lei Shi, Soumia Tayebi, Omar Abu Arqub, M. S. Osman, Praveen Agarwal, W. Mahamoud, Mahmoud Abdel-Aty, Mohammed Alhodaly
Summary: In this analysis, the high order cubic B-spline method is used to approximate solutions for fractional Painleve' and Bagley-Torvik equations. The approach considers different boundary set conditions. The discretization of the fractional model problems is achieved using a piecewise spline of a 3rd-degree polynomial. The spline method is demonstrated to be cost-efficient and precise in its calculations, making it suitable for various applications.
ALEXANDRIA ENGINEERING JOURNAL
(2023)
Article
Physics, Applied
Omar Abu Arqub, Banan Maayah
Summary: This paper introduces the TFMIADM model and its constraints, and reviews the formation of the model using the RKHSM computational approach. The solutions and modeling of the model based on Caputo's connotation of the partial time derivative are discussed. The paper presents the scores required to construct the method and discusses various theories such as solutions representations, convergence restriction, and order of error. The numeric-analytic solutions are expressed using the Fourier functions expansion rule, with the effectiveness and adaptation of the approach illustrated through drawings and tables. Viewpoints and highlights are presented alongside the most important modern references used.
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
(2023)
Article
Computer Science, Interdisciplinary Applications
Haneen Badawi, Omar Abu Arqub, Nabil Shawagfeh
Summary: This paper investigates the well-posedness of a class of FSIDEs utilizing the fractional Caputo-Fabrizio derivative. The proposed technique, based on the Legendre-shifted polynomials and collocation spectral method, effectively solves the stochastic equations subject to F-0-measurable independent parameters. Numerical applications confirm the accuracy and feasibility of the method, supporting the theoretical results.
INTERNATIONAL JOURNAL OF MODERN PHYSICS C
(2023)
Article
Computer Science, Interdisciplinary Applications
Wahiba Beghami, Banan Maayah, Omar Abu Arqub, Samia Bushnaq
Summary: In this study, the Laplace optimized decomposition scheme is proposed to approximate the solutions of the two-dimensional (2D) reaction-diffusion Brusselator model with noninteger derivative. The approximate solutions are obtained by applying the procedures of the Laplace inversion operator and truncating the optimized series, and are presented in tables and graphs. Numerical results demonstrate the efficiency, reliability, and accuracy of the technique for nonlinear systems of partial differential equations with noninteger-different order derivatives. Additionally, important notes and future plans are mentioned along with the key references.
INTERNATIONAL JOURNAL OF MODERN PHYSICS C
(2023)
Article
Computer Science, Interdisciplinary Applications
Omar Abu Arqub, Ahlem Ben Rabah, Shaher Momani
Summary: In this paper, the well-known Bagley-Torvik and Painleve models are solved numerically using the cubic B-spline polynomials approximation. Matrix operations and fundamental linear algebra are employed to transform the models into a computational scheme of linear and nonlinear algebraic equations. The accuracy and computational complexity of the scheme are analyzed based on extensive independent runs and statistical analysis.
INTERNATIONAL JOURNAL OF MODERN PHYSICS C
(2023)
Article
Mathematics
Shatha Hasan, Banan Maayah, Samia Bushnaq, Shaher Momani
Summary: The aim of this paper is to utilize the reproducing kernel Hilbert space method to solve linear and non-linear fuzzy integro-differential equations of fractional order under Caputo's H-differentiability. Analytic and approximate solutions are obtained in series form in the space W22 [a, b]. Several examples are provided to demonstrate the effectiveness and simplicity of the proposed method.
BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA
(2023)
Article
Mathematics, Interdisciplinary Applications
Shao-Wen Yao, Omar Abu Arqub, Soumia Tayebi, M. S. Osman, W. Mahmoud, Mustafa Inc, Hamed Alsulami
Summary: The goal and importance of this paper are to predict and build accurate and convincing numerical solutions for the time-fractional diffusion wave model in its singular version. The collective cubic uniform B-spline approach and standard finite difference approach are employed for this purpose. The paper demonstrates the applications of these approaches to fractional singular-type models in fluid dynamics and electromagnetics.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2023)
Article
Computer Science, Interdisciplinary Applications
Roumaissa Benseghir, Omar Abu Arqub, Banan Maayah
Summary: The aim of this analysis is to prove the existence and uniqueness of fractional conformable initial value time-delayed models incorporating time delays. The proof is based on Picard's iterative method and the fixed point theorem. Furthermore, a numerical method based on the reproducing kernel Hilbert approximation is proposed for solving fractional time-delayed problems. The results are presented in tables and figures for comparison with the exact solution.
INTERNATIONAL JOURNAL OF MODERN PHYSICS C
(2023)
Article
Mathematics, Applied
Omar Abu Arqub, Soumia Tayebi, Shaher Momani, Marwan Abukhaled
Summary: This paper introduces the abstract uses of conformable calculus in mathematics and practical applications in engineering and science, focusing on the cubic B-spline algorithm for solving conformable systems of differential boundary value problems. The effectiveness and efficiency of the spline approach are demonstrated through linear and nonlinear examples, showing that it requires less mathematical burden in problem-solving.
JOURNAL OF FUNCTION SPACES
(2023)
Article
Mathematics
M. Raheel, Khalid K. Ali, Asim Zafar, Ahmet Bekir, Omar Abu Arqub, Marwan Abukhaled
Summary: This article explores the analytical solutions of the economically important Ivancevic option pricing model (IOPM) using a new definition of derivative. The methods of exp(a) function, extended sinh-Gordon equation expansion (EShGEE), and extended (G'/G)-expansion are utilized for this purpose. The obtained solutions include dark, bright, dark-bright, periodic, singular, and other types of solutions, which are also verified using Mathematica tool. Some of the results are explained through 2-D, 3-D, and contour plots.
JOURNAL OF MATHEMATICS
(2023)
Article
Mathematics, Applied
Ahlem BenRabah, Omar Abu Arqub
Summary: The objective of this article is to provide an overview of B-splines collocation methods (BSCM) for obtaining practical analytical-numerical solutions to a range of regular/singular systems of initial constraint conditions (ICC). The conformable fractional derivatives are used to describe the fractional derivatives, and their basic theory is extensively utilized. The cubic B-splines and collocation methods are employed to simplify the computation of regular/singular systems of fractional order into a combination of linear/nonlinear algebraic equations. Numerical tests are conducted to demonstrate the technical statements and showcase the reliability, effectiveness, and applicability of the suggested procedure for solving such conformable systems models.
JOURNAL OF APPLIED ANALYSIS AND COMPUTATION
(2023)
