Article
Mathematics, Applied
Jabar S. Hassan, David Grow
Summary: In this paper, we introduce new reproducing kernel Hilbert spaces on a trapezoidal semi-infinite domain and establish uniform approximation results for solutions to nonhomogeneous hyperbolic partial differential equations. We also demonstrate the stability of these solutions with respect to the driver and provide an example to illustrate the efficiency and accuracy of our results.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Computer Science, Artificial Intelligence
Vladimir Vapnik, Rauf Izmailov
Summary: The paper explores reinforcement of SVM algorithms and justification of memorization mechanisms for generalization. It introduces modifications to existing SVM algorithms to improve classification performance. VC theory provides bounds for relative uniform convergence, aiding in more accurate estimate of the expected loss.
PATTERN RECOGNITION
(2021)
Article
Mathematics, Applied
Xiaoguang Zhang, Hong Du
Summary: An improved collocation method is proposed in the paper for solving a linear fractional integro-differential equation, which efficiently avoids ill-conditioned higher degree polynomials. The method aims to minimize the residual in sense of .C, providing superconvergence convergence order and stability analysis.
COMPUTATIONAL & APPLIED MATHEMATICS
(2021)
Article
Mathematics, Applied
Xuetong Su, Jiabao Yang, Huanmin Yao
Summary: This paper focuses on solving a class of quasilinear degenerate parabolic problems using the shifted Legendre reproducing kernel Galerkin method. The method linearizes the quasilinear term, discretizes the time derivative using finite difference scheme, constructs basis functions using shifted Legendre polynomials, and obtains the approximate solution using Galerkin method. The paper also discusses error estimates and stability analysis of the method, and provides numerical examples to demonstrate its feasibility and reliability.
APPLIED MATHEMATICS LETTERS
(2023)
Article
Mathematics, Applied
Nourhane Attia, Ali Akgul, Djamila Seba, Abdelkader Nour
Summary: This research work investigates new numerical solutions for essential fractional cancer tumor models using the reproducing kernel Hilbert space method. The method is easy to use and quickly calculates the numerical solutions for the problem. By utilizing Caputo fractional derivative, the study demonstrates the high competency and capacity of the suggested approach through convergence analysis.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Engineering, Multidisciplinary
Hao Cui, Yue Han, Hong Zheng, Shan Lin, Ruofan Wang
Summary: The paper explores the non-ordinary state-based peridynamic (NOSB-PD) method and its challenges such as numerical oscillations and boundary effects. It introduces the NOSB-PD method in the Galerkin framework and extends it by introducing the peridynamic differential operator (PDDO) approximation. The paper also compares the PDDO approximation with the reproducing kernel (RK) approximation and proposes a RK-PD coupling method to solve three-dimensional crack propagation problems.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Article
Materials Science, Multidisciplinary
Nourhane Attia, Ali Akgul, Djamila Seba, Abdelkader Nour, Muhammad Bilal Riaz
Summary: Based on the reproducing kernel theory, this paper presents an analytical approach for solving basic fractional ordinary differential equations using fractal fractional derivative with exponential decay kernel. The proposed method, reproducing kernel Hilbert space method (RKHSM), demonstrates high competency through convergence analysis. The results obtained from the RKHSM are compared with exact solutions, showcasing the impact of the fractal-fractional derivative with exponential decay on the outcomes and confirming the superior performance of the RKHSM.
RESULTS IN PHYSICS
(2022)
Article
Mathematics
Guan-Tie Deng, Yun Huang, Tao Qian
Summary: In this paper, the theory of Bergman kernel is extended to the weighted case, obtaining a general form of weighted Bergman reproducing kernel which can be used to calculate concrete Bergman kernel functions for specific weights and domains.
JOURNAL OF GEOMETRIC ANALYSIS
(2021)
Article
Mathematics, Applied
Wei Qu, Tao Qian, Haichou Li, Kehe Zhu
Summary: This study explores the best kernel approximation problem for analytic functions on the unit disk D in the reproducing kernel Hilbert space H, proving the existence of the best kernel approximation for weighted Bergman spaces with standard weights.
APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Engineering, Multidisciplinary
Nourhane Attia, Ali Akgul, Djamila Seba, Abdelkader Nour, Jihad Asad
Summary: We employ the reproducing kernel Hilbert space method to construct numerical solutions for fractional ordinary differential equations with fractal fractional derivative. The results demonstrate the effectiveness and superior performance of this method.
ALEXANDRIA ENGINEERING JOURNAL
(2022)
Article
Mathematics, Applied
Mojtaba Fardi
Summary: In this paper, the application of a kernel-based method in pseudo-spectral mode for multi-term and distributed order time-fractional diffusion equations is studied. Reproducing kernel functions are established in reproducing kernel Hilbert space using the theory of reproducing kernel. In the proposed method, a finite difference scheme is used in temporal space for semi-discrete configuration. The numerical solution is derived using the kernel-based PS method, and several numerical examples are provided to support the accuracy and efficiency of the proposed method, with the quality of the approximation calculated by absolute error and discrete error norms in the numerical experiments.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2023)
Article
Computer Science, Artificial Intelligence
Jiamin Liu, Wangli Xu, Fode Zhang, Heng Lian
Summary: Kernel Fisher discriminant (KFD) is a popular nonlinear extension of Fisher's linear discriminant, but its asymptotic properties have been rarely studied. In this study, we propose an operator-theoretical formulation of KFD and establish the convergence of the KFD solution to its population target. We also introduce a sketched estimation approach based on a m x n sketching matrix, which retains the asymptotic properties even when m is much smaller than n. Numerical results demonstrate the effectiveness of the sketched estimator.
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
(2023)
Article
Mathematics, Applied
Shiyv Wang, Xueqin Lv, Songyan He
Summary: Based on the reproducing kernel theory, this paper solves the nonlinear fourth order boundary value problem and verifies the effectiveness and accuracy of the approximate solution method through examples.
Article
Mathematics
Yue Wang, Baobin Wang, Chaoquan Peng, Xuefeng Li, Hong Yin
Summary: This paper studies the regularized Huber regression algorithm in a reproducing kernel Hilbert space (RKHS) and its applications in both fully supervised and semi-supervised learning schemes. The convergence properties of the algorithm with fully supervised data are provided, as well as the improved learning performance using a semi-supervised method.
Article
Mathematics, Interdisciplinary Applications
Dah-Chin Luor, Liang-Yu Hsieh
Summary: This paper investigates the connections between fractal interpolation functions (FIFs) and reproducing kernel Hilbert spaces (RKHSs). By establishing a fractal-type positive semi-definite kernel, it is shown that the span of linearly independent smooth FIFs is the corresponding RKHS. Furthermore, the nth derivatives of these FIFs, properties of related positive semi-definite kernels, and the importance of subspaces in curve-fitting applications are studied.
FRACTAL AND FRACTIONAL
(2023)
Article
Computer Science, Software Engineering
Muhammad Sajid Iqbal, Mustafa Inc, Sidra Ghazanfar, Nauman Ahmed
Summary: This paper mainly investigates the exact traveling waves fitting the mathematical model in electro-cardio-physiology. The source functions of noise-type are used in the proposed coupled system of nonlinear partial differential equations. The Ricatti-Bernoulli Sub-ODE method together with the Backlund extension is applied, and interesting plots for the obtained traveling waves and solitons are shown. The proposed model provides new applications for considerations under electric pulses or shocks, and the current method and modification of classical existence theory are applied for the first time to stochastic nonlinear problems in electro-cardiac physiology.
INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING
(2023)
Article
Physics, Multidisciplinary
Muhammad Sajid Iqbal, Nauman Ahmed, Rishi Naeem, Ali Akgul, Abdul Razzaque, Mustafa Inc, Hina Khurshid
Summary: This article analyzes a mathematical model that is described by a nonlinear partial differential equation governing the density of cancer cells. The model is two-dimensional and describes the dynamics of cancer cells under radiotherapy and its comparison with the absence of radiation effects. The 06-model expansion method is used to find exact solutions and the obtained results are simulated.
Article
Materials Science, Multidisciplinary
Shao-Wen Yao, Md Nuruzzaman, Dipankar Kumar, Nishat Tamanna, Mustafa Inc
Summary: This study derives lump solutions for a new integrable (3 + 1)-dimensional Boussinesq equation and its dimensionally reduced equations using the Hirota bilinear method and Maple. The derived lump solutions display two trough positions and one crest position, with the amplitudes and shapes of the lump waves remaining constant during propagation but changing their positions. Graphical outputs of the propagations of the obtained lump wave solutions illustrate the changes in trough and crest positions over time with constant velocity, with the free parameters of the model playing a significant role in altering the shapes and amplitudes of the waves.
RESULTS IN PHYSICS
(2023)
Article
Physics, Applied
Asif Waheed, Mustafa Inc, Nimra Bibi, Shumaila Javeed, Muhammad Zeb, Zain Ul Abadin Zafar
Summary: In this paper, the methods of exp-function and modified exp-function are used to generate various types of soliton solutions of the well-known Korteweg-de Vries (KdV) equation. These methods construct almost all types of soliton solutions that are rarely seen in history. The obtained solutions are verified for accuracy using symbolic computation program with Maple, and the physical appearance of the solutions is shown through 3D plots.
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
(2023)
Article
Computer Science, Artificial Intelligence
Izaz Ullah Khan, Jehanzeb Ali Shah, Muhammad Bilal, Faiza, Muhammad Saqib Khan, Sajid Shah, Ali Akgul
Summary: This study develops a machine learning model using chemical activated carbon (CAC) for the removal of reactive orange dye (Azo) RO16 from textile wastewater. The model takes into account the impact of concentration, temperature, time, pH, and dose on the removal efficiency. Multiple polynomial regression is used to fit the model to experimental data, achieving a close agreement with an R-squared value of 92%. The study finds that the baseline efficiency of using CAC for RO16 removal is 76.5%, and the second order response of the dose has the most significant impact on efficiency.
JOURNAL OF INTELLIGENT & FUZZY SYSTEMS
(2023)
Correction
Materials Science, Multidisciplinary
Tahira Sumbal Shaikh, Muhammad Zafarullah Baber, Nauman Ahmed, Muhammad Sajid Iqbal, Ali Akgul, Sayed M. El Din
RESULTS IN PHYSICS
(2023)
Article
Multidisciplinary Sciences
Hifza Iqbal, Muhammad Haroon Aftab, Ali Akgul, Zeeshan Saleem Mufti, Iram Yaqoob, Mustafa Bayram, Muhammad Bilal Riaz
Summary: Topological Indices are mathematical estimates that characterize biological structures based on atomic graphs and their real properties and chemical activities. These indices are graph isomorphism invariant. In various scientific fields such as biochemistry, chemical science, nano-medicine, and biotechnology, distance-based and eccentricity-connectivity (EC) based topological invariants of networks are useful for studying structure-property relationships and structure-activity relationships. They provide a solution for overcoming laboratory and equipment limitations for chemists and pharmacists. This paper presents the calculation of eccentricity-connectivity descriptors (ECD) and their related polynomials, total eccentricity-connectivity (TEC) polynomial, augmented eccentricity-connectivity (AEC) descriptor, and modified eccentricity-connectivity (MEC) descriptor for the hourglass benzenoid network.
Article
Computer Science, Artificial Intelligence
Muhammad Farman, Ali Akgul, Harish Garg, Dumitru Baleanu, Evren Hincal, Sundas Shahzeen
Summary: Monkeypox virus is a major cause of smallpox and cowpox infection. Researchers developed a fractional order model with the Mittag-Leffler kernel to analyze the dynamics of monkeypox virus infection. The model's uniqueness, positivity, and boundedness were confirmed using fixed point theory. The stability of the system at endemic and disease-free equilibrium points was established using a Lyapunov function. Numerical simulations demonstrated the accuracy of the suggested approaches.
Article
Multidisciplinary Sciences
Bahram Jalili, Amirali Shateri, Ali Akgul, Abdul Bariq, Zohreh Asadi, Payam Jalili, Davood Domiri Ganji
Summary: This study investigates the impact of heat radiation on magnetically-induced forced convection of nanofluid in a semi-porous channel. The research employs Akbari-Ganji's and Homotopy perturbation methods to analyze the effects of multiple parameters on the flow and heat transfer characteristics. The findings provide valuable insights into improving heat transfer in semi-porous channels.
SCIENTIFIC REPORTS
(2023)
Article
Materials Science, Multidisciplinary
Shuo Li, Samreen, Saif Ullah, Salman A. AlQahtani, Sayed M. Tag, Ali Akgul
Summary: The objective of this study was to develop a new mathematical model to examine the dynamics, future prediction, and effective control intervention of the emerging monkeypox disease in Nigeria. The model was parameterized using recent outbreak data and evaluated using a standard nonlinear least square method. The study analyzed the effectiveness of various control measures and identified critical parameters through mathematical analysis. An optimal control problem was also developed using time-dependent interventions. The findings emphasize the importance of strict personal protection and effective vaccination policies to eradicate the infection.
RESULTS IN PHYSICS
(2023)
Article
Engineering, Multidisciplinary
Mir Sajjad Hashemi, Ali Akguel, Ahmed Hassan, Mustafa Bayram
Summary: This paper focuses on a reduction technique to discover exact solutions for the generalized Camassa-Choi equation with temporal local M-derivative. Various types of exact solutions are presented along with their corresponding first integrals. The interactions between the orders of alpha and beta in the M-derivative are taken into account and depicted graphically for the derived solutions. In certain situations, exact solutions can be obtained for any value of n.
ALEXANDRIA ENGINEERING JOURNAL
(2023)
Article
Mathematics, Interdisciplinary Applications
Nayyar Mehmood, Ahsan Abbas, Ali Akgul, Thabet Abdeljawad, Manara A. Alqudah
Summary: In this paper, the existence of solutions for a coupled system of nonlinear fractional differential equations is studied using Krasnoselskii's fixed point theorem. Uniqueness is discussed with the help of the Banach contraction principle. The criteria for the Hyers-Ulam stability of the given boundary value problem is also examined, and examples are provided to validate the results.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2023)
Article
Mathematics, Interdisciplinary Applications
Ri Zhang, Nehad Ali Shah, Essam R. El-Zahar, Ali Akgul, Jae Dong Chung
Summary: This work introduces a new semi-analytical method, the variational iteration transform method, for investigating fractional-order Emden-Fowler equations. The Shehu transformation and the iterative method are utilized to solve the given problems. The proposed method demonstrates higher accuracy compared to other techniques and does not require additional calculations. Numerical problems validate the effectiveness of the suggested method in solving nonlinear fractional-order problems.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2023)
Article
Mathematics, Applied
Rashid Ali, Ali Akgul
Summary: This study introduces and analyzes a new generalized accelerated overrelaxation method (NGAOR) for solving linear complementarity problems (LCPs), and proves the convergence of the method under certain conditions. Numerical experiments demonstrate the effectiveness and efficiency of the proposed method.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Hamood Ur Rehman, Muhammad Imran Asjad, Ifrah Iqbal, Ali Akgul
Summary: In this study, the Sardar subequation method (SSM) and conformable derivative (CD) are utilized to seek exact solutions of the (2 + 1)-dimensional space-time fractional Zoomeron equation (FZE). Various soliton solutions including bright, dark, singular, periodic singular, and bright-dark hybrid solitons are obtained. The proposed method is simple and effective for solving nonlinear fractional differential equations.
INTERNATIONAL JOURNAL OF APPLIED NONLINEAR SCIENCE
(2023)
