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
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
Mathematics, Interdisciplinary Applications
Chengcai Cai, Yongjun Shen, Shaofang Wen
Summary: The dynamic characteristics and stability of a fractional-order van der Pol oscillator under simultaneously primary and super-harmonic resonance are analyzed using the multiscale method. The first-order approximate analytical solution of the system is obtained and verified by numerical simulation. The concepts of equivalent linear damping and equivalent linear stiffness are proposed to understand the roles of fractional parameters. The stability region, equilibrium points, and the influences of fractional order and coefficient on the system are discussed.
CHAOS SOLITONS & FRACTALS
(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
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
Mathematics, Applied
Sami Aljhani, Mohd Salmi Md Noorani, Redouane Douaifia, Salem Abdelmalek
Summary: In this paper, a numerical scheme of the predictor-corrector type is proposed to solve nonlinear fractional initial value problems using the Atangana-Baleanu derivative defined in Caputo sense. The method utilizes Lagrangian quadratic polynomials to approximate the nonlinearity in the Volterra integral, obtained through the properties of the ABC-fractional derivative. The proposed method provides a high-accuracy corrector formula and an explicit predictor formula, with the memory term computed only once for both phases, indicating low cost.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
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
Engineering, Multidisciplinary
Aisha F. Fareed, Mourad S. Semary, Hany N. Hassan
Summary: This paper introduces a computationally efficient approach for solving fractional differential equations with the Atangana-Baleanu operator. The proposed method is suitable for a class of fractional differential equations, covering a wide range of integer and fractional order equations, and is applicable to nonlinear differential equations.
ALEXANDRIA ENGINEERING JOURNAL
(2022)
Article
Physics, Multidisciplinary
H. Yepez-Martinez, J. F. Gomez-Aguilar, Mustafa Inc
Summary: The main goal of this work is to propose a new modified version of the Atangana-Baleanu fractional derivative with Mittag-Leffler non-singular kernel and strong memory. This modification is advantageous for specific initial conditions and can be applied in solving nonlinear fractional differential equations using perturbative analytical methods. The fulfillment of initial conditions plays a central role in obtaining accurate solutions and the new fractional derivative can contribute to more accurate mathematical modeling in various fields.
Article
Engineering, Multidisciplinary
M. M. El-Dessoky, Muhammad Altaf Khan
Summary: Mathematical modeling of infectious diseases with non-integer order is gaining attention, with fractional derivative models proving more powerful and effective in overcoming limitations of classical models. New operators such as fractal-fractional ones have been introduced to better model problems in science and engineering, particularly in epidemic modeling like dengue fever.
ALEXANDRIA ENGINEERING JOURNAL
(2022)
Article
Mathematics, Applied
Saima Rashid, Sobia Sultana, Bushra Kanwal, Fahd Jarad, Aasma Khalid
Summary: This study evaluates the suitability of the Elzaki Adomian decomposition method for the fractional-order Swift-Hohenberg model and successfully constructs approximate analytical solutions for fuzzy fractional partial differential equations.
Article
Engineering, Multidisciplinary
Amjad Shaikh, Kottakkaran Sooppy Nisar, Vikas Jadhav, Sayed K. Elagan, Mohammed Zakarya
Summary: This paper presents and investigates a mathematical model describing the HIV/AIDS transmission dynamics in the presence of an aware community using a specific fractional differential operator. The existence and uniqueness conditions of the model are obtained through the fixed point theorem, and an approximate solution is obtained using the iterative Laplace transform approach. The necessary conditions for disease control and numerical simulations for different fractional orders are explored, along with a comparison between numerical results obtained using different operators.
ALEXANDRIA ENGINEERING JOURNAL
(2022)
Article
Mathematics, Interdisciplinary Applications
Zhao Li
Summary: This paper studies the dynamical behavior, optical soliton solution, and traveling wave solution of the fractional Biswas-Arshed equation with the beta time derivative using the theory of planar dynamical systems. By simplifying the equation and plotting phase portraits, the optical soliton solution and traveling wave solution are obtained.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Interdisciplinary Applications
Esmehan Ucar, Sumeyra Ucar, Firat Evirgen, Necati Ozdemir
Summary: This study introduces a special model for spreading malicious worms through SMS, combining the AB derivative and the SAIDR model. The existence and uniqueness of solutions for the model, as well as the stability analysis, are demonstrated using the Banach fixed point theorem. The effectiveness of fractional derivatives is shown through numerical graphics by varying the fractional-order theta.
FRACTAL AND FRACTIONAL
(2021)
Article
Mathematics, Interdisciplinary Applications
Aziz Khan, Thabet Abdeljawad, Hasib Khan
Summary: This paper presents a numerical and analytical investigation of a fractional-order model for HCV transmission, using Lagrange's interpolation polynomial technique for numerical outcomes. The proposed method shows high precision and low computing cost, with numerical results containing dynamics of the previous integer-order model as a special case. Numerical solutions for the fractional-order HCV model are implemented to demonstrate results graphically.
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
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
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
Engineering, Mechanical
Marwa Laoubi, Zaid Odibat, Banan Maayah
Summary: In this paper, the optimized decomposition method is modified and extended to handle nonlinear fractional differential equations. Two optimized decomposition algorithms are introduced to solve initial value problems for nonlinear fractional ordinary differential equations and partial differential equations. Comparative study shows that the proposed algorithms have better accuracy and convergence compared to the Adomian decomposition method.
JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS
(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
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)
Article
Mathematics, Applied
Emad H. M. Zahran, Omar Abu Arqub, Ahmet Bekir, Marwan Abukhaled
Summary: The main purpose of this study was to generate abundant new types of soliton solutions for the Radhakrishnan-Kundu-Lakshmanan equation, which represents unstable optical solitons that result from optical propagations through birefringent fibers. These new soliton solutions exhibit bright, dark, W-shaped, M-shaped, periodic trigonometric, and hyperbolic behaviors that have not been observed before using any other method. Four different techniques, including the extended simple equation method, the Paul-Painleve approach method, the Ricatti-Bernoulli-sub ODE, and the solitary wave ansatz method, were used to detect these new solitons. These new solitons will contribute to future studies on both this model and optical propagations through birefringent fiber.
