Article
Mathematics, Interdisciplinary Applications
Mohamed Fathy, K. M. Abdelgaber
Summary: This paper presents and applies the Galerkin method to obtain semi-analytical solutions of quadratic Riccati and Bagley-Torvik differential equations in fractional order. New theorems are proposed to optimize the efficiency of the method by minimizing the generated residual. The proposed method is compared with other methods through solving initial value problems of different fractional orders, and the results are illustrated using tables and figures. The Legendre-Galerkin method is found to be efficient and reliable for these problems.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Applied
Jingjun Zhao, Wenjiao Zhao, Yang Xu
Summary: This work focuses on the numerical solution of initial and boundary value problems for space-time fractional advection-diffusion equations. The well-posedness of weak solutions is proven using the Lax-Milgram lemma. Two fully discrete methods are established, combining a hybridizable discontinuous Galerkin approach in the spatial direction and two finite difference schemes in the temporal direction: L1 formula and the weighted and shifted Grunwald-Letnikov formula. The stability and convergence analyses of these methods are derived in detail, and several numerical experiments are provided to illustrate the theoretical results.
APPLIED MATHEMATICS AND COMPUTATION
(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
Mathematics, Applied
Qinxu Ding, Patricia J. Y. Wong
Summary: This paper develops a higher order numerical method for the fractional Bagley-Torvik equation, utilizing a new fourth-order approximation for the fractional derivative and a discrete cubic spline approach. The theoretical convergence order of the method is shown to improve upon previous work. Five examples are provided to demonstrate the efficiency of the method and compare it with others in the literature.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics, Applied
Murugesan Meganathan, Thabet Abdeljawad, M. Motawi Khashan, Gnanaprakasam Britto Antony Xavier, Fahd Jarad
Summary: This research introduces a discrete version of the fractional Bagley-Torvik equation and obtains solutions using the nabla discrete Laplace transform. The solutions are expressed in terms of Mittag-Leffler functions with three parameters and are numerically handled for specific examples.
ADVANCES IN DIFFERENCE EQUATIONS
(2021)
Article
Materials Science, Multidisciplinary
Kamran, Muhammad Asif, Kamal Shah, Bahaaeldin Abdalla, Thabet Abdeljawad
Summary: This article aims to solve the Bagley-Torvik equation involving the Atangana-Baleanu derivative using the Laplace transform method. The Laplace transform is an effective tool for solving differential equations, but sometimes leads to solutions in the Laplace domain that cannot be inverted back to the time domain analytically. Therefore, numerical methods are used to convert the solution from the Laplace domain to the time domain. Four numerical inverse Laplace transform methods are utilized, and their accuracy and efficiency are validated through four test problems. The computational results are presented using tables and figures, and compared with other methods in the literature to demonstrate the superiority of the proposed methods.
RESULTS IN PHYSICS
(2023)
Article
Mathematics, Applied
Aycil Cesmelioglu, Jeonghun J. Lee, Sander Rhebergen
Summary: We introduce and analyze a hybridizable discontinuous Galerkin finite element method for the coupled Stokes-Biot problem. The method has the property that the discrete velocities and displacements satisfy the compressibility equations pointwise on the elements. We prove well-posedness of the discretization and provide a priori error estimates that demonstrate the method is free of volumetric locking. Numerical examples further demonstrate optimal rates of convergence for all unknowns and locking-free discretization.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
Article
Mathematics, Interdisciplinary Applications
Nelson Vieira, M. Manuela Rodrigues, Milton Ferreira
Summary: Motivated by the increase in practical applications of fractional calculus, this study investigates the classical gradient method from the perspective of the ?-Hilfer derivative. Multiple definitions of fractional derivatives found in the literature are covered in this study. Convergence of the ?-Hilfer continuous fractional gradient method is studied for both strongly and non-strongly convex cases. The proposed ?-Hilfer fractional order gradient method, developed using a series representation of the target function, is tested and analyzed using benchmark functions, and shows improved speed and accuracy compared to previous methods.
FRACTAL AND FRACTIONAL
(2023)
Article
Mathematics, Interdisciplinary Applications
Haiyong Xu, Lihong Zhang, Guotao Wang
Summary: This paper investigates the existence of extremal solutions for a nonlinear boundary value problem involving the Caputo-Fabrizio-type fractional differential operator. By utilizing a new inequality and applying a monotone iterative technique with upper and lower solutions, the main result is obtained. The paper concludes with an illustrative example.
FRACTAL AND FRACTIONAL
(2022)
Article
Computer Science, Interdisciplinary Applications
Carlos A. Pereira, Brian C. Vermeire
Summary: This paper presents a unified framework for hybridizing flux reconstruction (FR) schemes and analyzes the performance and accuracy of hybridized flux reconstruction (HFR) and interior-embedded flux reconstruction (EFR) methods on quadrilateral elements. It is found that EFR methods generally introduce additional numerical error but behave closer to FR methods for higher orders. The choice of correction function has an impact on the performance of the implicit solver, with EFR methods showing potential for higher accuracy and reduced computational cost.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Mathematics, Interdisciplinary Applications
Ahmed Z. Amin, Mohamed A. Abdelkawy, Emad Solouma, Ibrahim Al-Dayel
Summary: This paper proposes a numerical solution based on the shifted Legendre Gauss-Lobatto collocation technique for the non-linear distributed-order fractional Bagley-Torvik differential equation, and verifies its accuracy through numerical examples.
FRACTAL AND FRACTIONAL
(2023)
Article
Mathematics, Applied
Shatha Hasan, Nadir Djeddi, Mohammed Al-Smadi, Shrideh Al-Omari, Shaher Momani, Andreea Fulga
Summary: This paper investigates the generalized Bagley-Torvik equation based on the Caputo-Fabrizio fractional derivative concept using a modified reproducing kernel Hilbert space treatment. By reformulating the problem as a system of fractional differential equations while preserving the second type of these equations, the study establishes reproducing kernel functions to construct an orthogonal system for both analytical and approximate solutions in the appropriate Hilbert spaces. The proposed method shows accuracy, efficiency, and reliability in solving various real-life problems through numerical examples.
ADVANCES IN DIFFERENCE EQUATIONS
(2021)
Article
Mathematics, Applied
Hazrat Ali, Md. Kamrujjaman, Afroza Shirin
Summary: In this paper, a new numerical solution scheme for the Bagley-Torvik equation of order (0, 2) based on the finite element method is developed, showing its accuracy, efficiency, and simplicity through numerical examples and results. The method's accuracy is better than existing methods, providing guidance for solving fractional-order boundary value problems.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2021)
Article
Multidisciplinary Sciences
Diego Caratelli, Pierpaolo Natalini, Paolo Emilio Ricci, Dongfang Li, Junesang Choi
Summary: This paper approximates the solution of a generalized form of the Bagley-Torvik equation using Taylor's expansions in fractional powers, and verifies the findings by studying the fractional Laguerre-type logistic equation.
Article
Multidisciplinary Sciences
Saeed Althubiti, Abdelaziz Mennouni
Summary: This study proposes an effective method for approximating solutions to the Bagley-Torvik system and obtains interesting original results.
Article
Mathematics, Applied
Burak Aksoylu, Fatih Celiker, Orsan Kilicer
ADVANCES IN COMPUTATIONAL MATHEMATICS
(2019)
Article
Mathematics, Applied
Yaprak Guldogan Dericioglu, Muhammet Kurulay
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2019)
Article
Mathematics, Applied
Mehmet Fatih Karaaslan
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2019)
Article
Telecommunications
Ala-Eddine Benrazek, Zineddine Kouahla, Brahim Farou, Mohamed Amine Ferrag, Hamid Seridi, Muhammet Kurulay
TRANSACTIONS ON EMERGING TELECOMMUNICATIONS TECHNOLOGIES
(2020)
Article
Mathematics, Applied
Mourad Ghiat, Hamza Guebbai, Muhammet Kurulay, Sami Segni
COMPUTATIONAL & APPLIED MATHEMATICS
(2020)
Article
Mathematics, Applied
M. Moumen Bekkouche, H. Guebbai, M. Kurulay
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2020)
Article
Mathematics, Applied
Veli Shakhmurov, Muhammet Kurulay
Summary: This paper studies the L-p coercive properties of a nonlocal fractional elliptic equation and proves that the fractional elliptic operator generated by this equation is sectorial in L-p space and also is a generator of an analytic semigroup. Moreover, by using the L-p separability properties of the given elliptic operator, the maximal regularity of the corresponding nonlocal fractional parabolic equation is established.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics, Applied
Shakir Ali, Amal S. Alali, Mohammad Jeelani, Muhammet Kurulay, Elif Segah oeztas, Pushpendra Sharma
Summary: The main goal of this article is to study the structural properties of cyclic codes over a finite ring R = F-q[u(1), u(2)]/(u(1)(2) - alpha(2), u(2)(2) - beta(2), u(1)u(2)- u(2)u(1)), where F-q is a field of order q, q is a power of an odd prime p, and alpha and beta are two non-zero elements of F-q. We decompose the ring R into Delta R-1 plus Delta R-2 plus Delta R-3 plus Delta R-4 using orthogonal idempotents Delta(1), Delta(2), Delta(3), and Delta(4), and construct quantum-error-correcting (QEC) codes over R. As an application, we construct some optimal LCD codes.
Article
Biotechnology & Applied Microbiology
Veli B. Shakhmurov, Muhammet Kurulay, Aida Sahmurova, Mustafa Can Gursesli, Antonio Lanata
Summary: This study utilized phase-space analysis to investigate the interaction between virus and immune response in a mathematical model of tumor growth. A dynamic model was used to mathematically determine the relationship between uninfected cells, infected cells, effector immune cells, and free viruses. Stability analysis of the system and the Lyapunov stability of the equilibrium points were revealed, and all endemic equilibrium point models were derived. The stability behavior and range of attraction sets of the nonlinear systems in our model were investigated. Furthermore, a global stability analysis was proven for both disease-free equilibria and endemic equilibria.
BIOENGINEERING-BASEL
(2023)
Article
Computer Science, Information Systems
Zineddine Kouahla, Ala-Eddine Benrazek, Mohamed Amine Ferrag, Brahim Farou, Hamid Seridi, Muhammet Kurulay, Adeel Anjum, Alia Asheralieva
Summary: This paper examines and reviews existing indexing techniques for large-scale data, proposes a taxonomy for researchers to select techniques as the basis for designing new indexing schemes, presents real-world applications in various fields, and discusses open problems and research challenges.
Article
Mathematics
M. Moumen Bekkouche, H. Guebbai, M. Kurulay, S. Benmahmoud
Summary: This article introduces a new fractional integral associated with the Caputo-Fabrizio fractional derivative, and demonstrates its application by solving a fractional boundary value problem. Additionally, a Matlab script for solving the BVP is provided.
RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO
(2021)
Proceedings Paper
Engineering, Electrical & Electronic
Misrat Yesiltepe, Akthar Jamil, Jawad Rasheed, Muhammet Kurulay
2019 11TH INTERNATIONAL CONFERENCE ON ELECTRICAL AND ELECTRONICS ENGINEERING (ELECO 2019)
(2019)
Proceedings Paper
Computer Science, Hardware & Architecture
Mohamed Amine Ferrag, Zineddine Kouahla, Hamid Seridi, Muhammet Kurulay
2019 4TH INTERNATIONAL CONFERENCE ON NETWORKING AND ADVANCED SYSTEMS (ICNAS 2019)
(2019)
Article
Telecommunications
Ala-Eddine Benrazek, Brahim Farou, Hamid Seridi, Zineddine Kouahla, Muhammet Kurulay
IET WIRELESS SENSOR SYSTEMS
(2019)
Article
Mathematics
Mehmet Fatih Karaaslan
Summary: In this paper, the existence-uniqueness of solutions to the second-order linear Fredholm integrodifferential equation with Dirichlet boundary condition is obtained using the hybridizable discontinuous Galerkin method. Necessary and sufficient conditions based on stabilization parameter and kernel function are provided to ensure the existence-uniqueness of the approximate solution. Numerical examples are conducted to assess the performance of the method, showing its reliability and feasibility compared to existing methods.
TURKISH JOURNAL OF MATHEMATICS
(2021)
Article
Mathematics, Applied
Peter Frolkovic, Nikola Gajdosova
Summary: This paper presents compact semi-implicit finite difference schemes for solving advection problems using level set methods. Through numerical tests and stability analysis, the accuracy and stability of the proposed schemes are verified.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Md. Rajib Arefin, Jun Tanimoto
Summary: Human behaviors are strongly influenced by social norms, and this study shows that injunctive social norms can lead to bi-stability in evolutionary games. Different games exhibit different outcomes, with some showing the possibility of coexistence or a stable equilibrium.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Dingyi Du, Chunhong Fu, Qingxiang Xu
Summary: A correction and improvement are made on a recent joint work by the second and third authors. An optimal perturbation bound is also clarified for certain 2 x 2 Hermitian matrices.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Pingrui Zhang, Xiaoyun Jiang, Junqing Jia
Summary: In this study, improved uniform error bounds are developed for the long-time dynamics of the nonlinear space fractional Dirac equation in two dimensions. The equation is discretized in time using the Strang splitting method and in space using the Fourier pseudospectral method. The major local truncation error of the numerical methods is established, and improved uniform error estimates are rigorously demonstrated for the semi-discrete scheme and full-discretization. Numerical investigations are presented to verify the error bounds and illustrate the long-time dynamical behaviors of the equation with honeycomb lattice potentials.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Kuan Zou, Wenchen Han, Lan Zhang, Changwei Huang
Summary: This research extends the spatial PGG on hypergraphs and allows cooperators to allocate investments unevenly. The results show that allocating more resources to profitable groups can effectively promote cooperation. Additionally, a moderate negative value of investment preference leads to the lowest level of cooperation.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Kui Du
Summary: This article introduces two new regularized randomized iterative algorithms for finding solutions with certain structures of a linear system ABx = b. Compared to other randomized iterative algorithms, these new algorithms can find sparse solutions and have better performance.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Shadi Malek Bagomghaleh, Saeed Pishbin, Gholamhossein Gholami
Summary: This study combines the concept of vanishing delay arguments with a linear system of integral-algebraic equations (IAEs) for the first time. The piecewise collocation scheme is used to numerically solve the Hessenberg type IAEs system with vanishing delays. Well-established results regarding regularity, existence, uniqueness, and convergence of the solution are presented. Two test problems are studied to verify the theoretical achievements in practice.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Qi Hu, Tao Jin, Yulian Jiang, Xingwen Liu
Summary: Public supervision plays an important role in guiding and influencing individual behavior. This study proposes a reputation incentives mechanism with public supervision, where each player has the authority to evaluate others. Numerical simulations show that reputation provides positive incentives for cooperation.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Werner M. Seiler, Matthias Seiss
Summary: This article proposes a geometric approach for the numerical integration of (systems of) quasi-linear differential equations with singular initial and boundary value problems. It transforms the original problem into computing the unstable manifold at a stationary point of an associated vector field, allowing efficient and robust solutions. Additionally, the shooting method is employed for boundary value problems. Examples of (generalized) Lane-Emden equations and the Thomas-Fermi equation are discussed.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Lisandro A. Raviola, Mariano F. De Leo
Summary: We evaluated the performance of novel numerical methods for solving one-dimensional nonlinear fractional dispersive and dissipative evolution equations and showed that the proposed methods are effective in terms of accuracy and computational cost. They can be applied to both irreversible models and dissipative solitons, offering a promising alternative for solving a wide range of evolutionary partial differential equations.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Yong Wang, Jie Zhong, Qinyao Pan, Ning Li
Summary: This paper studies the set stability of Boolean networks using the semi-tensor product of matrices. It introduces an index-vector and an algorithm to verify and achieve set stability, and proposes a hybrid pinning control technique to reduce computational complexity. The issue of synchronization is also discussed, and simulations are presented to demonstrate the effectiveness of the results obtained.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Ling Cheng, Sirui Zhang, Yingchun Wang
Summary: This paper considers the optimal capacity allocation problem of integrated energy systems (IESs) with power-gas systems for clean energy consumption. It establishes power-gas network models with equality and inequality constraints, and designs a novel full distributed cooperative optimal regulation scheme to tackle this problem. A distributed projection operator is developed to handle the inequality constraints in IESs. The simulation demonstrates the effectiveness of the distributed optimization approach.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Abdurrahim Toktas, Ugur Erkan, Suo Gao, Chanil Pak
Summary: This study proposes a novel image encryption scheme based on the Bessel map, which ensures the security and randomness of the ciphered images through the chaotic characteristics and complexity of the Bessel map.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Xinjie Fu, Jinrong Wang
Summary: In this paper, we establish an SAIQR epidemic network model and explore the global stability of the disease in both disease-free and endemic equilibria. We also consider the control of epidemic transmission through non-instantaneous impulsive vaccination and demonstrate the sustainability of the model. Finally, we validate the results through numerical simulations using a scale-free network.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Maria Han Veiga, Lorenzo Micalizzi, Davide Torlo
Summary: The paper focuses on the iterative discretization of weak formulations in the context of ODE problems. Several strategies to improve the accuracy of the method are proposed, and the method is combined with a Deferred Correction framework to introduce efficient p-adaptive modifications. Analytical and numerical results demonstrate the stability and computational efficiency of the modified methods.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
