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, Interdisciplinary Applications
Xiaozhong Liao, Manjie Ran, Donghui Yu, Da Lin, Ruocen Yang
Summary: This paper presents a time-domain mathematical model of the Buck converter using the non-singular fractional derivative proposed by Caputo and Fabrizio. The chaotic behaviors of the system are studied, and the implementation of the fractional-order Buck converter in analog circuits is established. The results of circuit simulations effectively validate the accuracy of the previous theoretical analysis.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Engineering, Multidisciplinary
Yasir Khan, Muhammad Altaf Khan, Fatmawati, Naeem Faraz
Summary: This study investigates a competition model using Caputo-Fabrizio type of fractional derivative with a Newton based polynomial approach, analyzing the stability of fixed points and presenting real parameters from actual bank data. The study provides a new data fitting method and identifies the suitable order of rho for fitting based on graphical illustrations, showing the effectiveness of the proposed new scheme.
ALEXANDRIA ENGINEERING JOURNAL
(2021)
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
Yu-Ming Chu, Muhammad Farooq Khan, Saif Ullah, Syed Azhar Ali Shah, Muhammad Farooq, Mustafa bin Mamat
Summary: Vector-host diseases outbreak is a major concern for public health, and this study presents a compartmental transmission model to explore the dynamics of these diseases. The model formulation considers the saturated incidence rate instead of bilinear and saturated treatment function to enhance its biological suitability. The equilibrium points and basic reproduction number of the model are investigated, and the existence and uniqueness are demonstrated using the fixed point approach. The model simulations illustrate the impact of arbitrary fractional order and other important parameters on the disease dynamics and minimization.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Interdisciplinary Applications
Fei Gao, Xiling Li, Wenqin Li, Xianjin Zhou
Summary: Mathematical models are crucial in understanding the dynamics of infectious diseases, and a new mathematical model for HBV based on Caputo-Fabrizio fractional derivative with immune delay is introduced in this paper. The existence and uniqueness of the model solutions are proved using Laplace transform and fixed point theorem, with discussions on positivity and boundedness of the solutions. Stability and iterative solution of the fractional order model of HBV are analyzed using Sumudu transform and Picard iteration.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Applied
Zhoujin Cui
Summary: This paper discusses the solutions to typical nonlinear fractional differential equations and obtains implicit analytical solutions. The Caputo-Fabrizio form of fractional derivative is considered, which has a nonsingular kernel. The calculation results of different fractional orders are compared through images. Furthermore, by comparing the results obtained in this paper with those under Caputo fractional derivative, it is found that the solutions change relatively gently under Caputo-Fabrizio fractional derivative. It can be concluded that the selection of appropriate fractional derivatives and fractional orders is crucial in the modeling process.
Article
Mathematics
Jennifer Bravo, Carlos Lizama
Summary: This paper investigates the solution to an abstract Cauchy problem with a injective closed linear operator A defined in a Banach space X. By introducing the Caputo-Fabrizio fractional derivative, the problem is transformed into a first-order abstract Cauchy problem, and the expression for the unique solution is derived. Furthermore, the convergence and existence of the solution are studied, leading to some conclusions about the initial conditions and parameters.
Article
Mathematics, Applied
Fazal Haq, Ibrahim Mahariq, Thabet Abdeljawad, Nabil Maliki
Summary: In this manuscript, the existence and semi-analytical solutions of the fractional-order vector-born disease model were investigated using the Caputo-Fabrizio fractional derivative. The results were obtained through fixed-point theory and Laplace Adomain decomposition method, showing rapid convergence to the exact solution. A comparison with integer-order derivatives was made, with the dynamics of the solution interpreted graphically.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2021)
Article
Computer Science, Interdisciplinary Applications
Leilei Wei, Wenbo Li
Summary: In this paper, an accurate numerical scheme for solving a class of variable-order fractional diffusion equation based on the Caputo-Fabrizio fractional derivative is constructed and investigated. The proposed scheme shows stability and L-2 convergence, with an accuracy-order of O(tau + h(k+1)). Numerical tests validate the theoretical analysis and efficiency of the algorithm.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2021)
Article
Engineering, Multidisciplinary
Nesrine Harrouche, Shaher Momani, Shatha Hasan, Mohammed Al-Smadi
Summary: This paper introduces an advanced numerical-analytical approach for solving fuzzy fractional differential equations in the medical sector, utilizing reproducing kernel algorithm to generate analytical solutions. The method's effectiveness is demonstrated through theoretical and analytical analysis, as well as stability results based on reproducing kernel theory. Numerical simulations validate the algorithm's reliability in solving fuzzy models, particularly in drug pharmacokinetic models.
ALEXANDRIA ENGINEERING JOURNAL
(2021)
Article
Engineering, Mechanical
Yuhang Pan
Summary: This study analyzed a four-dimensional fractional hyperchaotic model using general Riemann-Liouville-Caputo fractal-fractional derivative. New operators were constructed for modeling the Qi hyperchaotic fractional attractor, with numerical solutions obtained using an efficient scheme. The results showed strange and new attractors with self-similarities, demonstrating crossover effects between different derivatives.
NONLINEAR DYNAMICS
(2021)
Article
Mathematics, Applied
Vivekananda Rayanki, Izhar Ahmad, Krishna Kummari
Summary: This article focuses on a specific type of interval-valued variational programming problem (IVVCF) involving the Caputo-Fabrizio fractional derivative. It discusses the concept of a LU optimal solution for this type of problem. The necessary and sufficient optimality conditions of the Karush-Kuhn-Tucker type are constructed using the LU optimal concept for an (IVVCF). Additionally, a Wolfe-type dual model is developed for an (IVVCF) and the required duality theorems are discussed.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Youssouf Massoun
Summary: This paper presents an analytical study of the epidemic pine wilt disease model using a Caputo-Fabrizio type fractional order. The basic properties of the fractional differential equation and the model are discussed, and numerical solutions are obtained using the homotopy analysis transform method. The results are presented in graphical form.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics, Interdisciplinary Applications
Kolade M. Owolabi
Summary: Pattern formation processes in non-integer order systems are studied with efficient numerical schemes to solve time-fractional reaction-diffusion equations, showcasing the dynamic richness in pattern formation in different dimensional spaces. Experimental results mimic various Pseudoplatystoma catfish structures and provide results for different values of fractional power.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Engineering, Civil
Muge Albayrak, Daniel Willi, Sebastien Guillaume
Summary: This study determines the precision and accuracy of the QDaedalus system based on observations at two locations in Switzerland. The precision was found to be 0.1'' through extensive observations, while the accuracy was established through parallel observations and found to be within 0.1''. Notably, a large systematic trend was observed in the N-S DoV data at one of the test stations.
Article
Food Science & Technology
Hamza Alasalvar, Murat Kaya, Serap Berktas, Bulent Basyigit, Mustafa Cam
Summary: This study investigated the extraction of bioactive compounds from lemon peel using pressurised hot water extraction (PHWE). The results showed that PHWE at specific temperature and time conditions could selectively extract eriocitrin and hesperidin, resulting in higher total phenolic content and antioxidant capacities compared to conventional extraction methods.
INTERNATIONAL JOURNAL OF FOOD SCIENCE AND TECHNOLOGY
(2023)
Article
Environmental Sciences
Ibrahim Yenigun, Ali Volkan Bilgili, Halil Ibrahim Senol, Abdullah Yenigun
Summary: Underground water resources are vital for mankind, used for drinking water and agricultural irrigation. This study investigates the changes in groundwater quality in the Upper Mesopotamian region, which has a semi-arid climate and important past civilizations. Samples from selected wells in the Mardin Kiziltepe Plain were collected and analyzed for water quality classifications. The results show no non-standard values and will provide important data for future irrigation projects.
ENVIRONMENTAL MONITORING AND ASSESSMENT
(2023)
Article
Physics, Applied
Nauman Raza, Amna Batool, Haci Mehmet Baskonus, Fernando Vidal S. Causanilles
Summary: In this paper, new extended generalized Kudryashov and improved tan(θ/2) expansion approaches are used to investigate Kerr law nonlinearity in the extended Gerdjikov-Ivanov equation in a dense wavelength division multiplexed system. These methods rely on a traveling wave transformation and an auxiliary equation. The methods successfully extract trigonometric, rational and hyperbolic solutions, and impose appropriate conditions on parameters. A graphical description of newly discovered solutions is also presented to explain the dynamics of soliton profiles, which exhibits distinct physical significance. These methods are recognized as useful and influential tools for creating solitary wave solutions to nonlinear problems in the mathematical sciences.
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
(2023)
Article
Mathematics, Applied
Sanjay Bhatter, Shyamsunder Kumawat, Kamlesh Jangid, S. D. Purohit, Haci Mehmet Baskonus
Summary: This study introduces and investigates a fractional integral operator with an I-function in its kernel, which is used to solve fractional differential equations. Fractional differential equations have various particular cases that represent different physical phenomena. Many problems in mathematical physics, biology, engineering, and chemistry can be identified and solved using fractional differential equations. The study first solves the fractional differential equation and integral operator for the incomplete I-function (IIF) and the generalized composite fractional derivative (GCFD). Several important exceptional cases are then discovered and investigated. The significant finding of this study is a Volterra-type first-order integer differential equation that clearly describes the unsaturated nature of free-electron lasers.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Engineering, Electrical & Electronic
Assad Ayub, Zulqurnain Sabir, Salem Ben Said, Haci Mehmet Baskonus, R. Sadat, Mohamed R. Ali
Summary: The aim of this article is to explore the characteristics of fluid flow using melting and entropy generation on the Riga plate. Cross fluid is used to examine the behaviors of high and low deformations under external forces. The mechanisms of heat transport, such as melting conditions, viscous dissipation, and thermal radiation are investigated. The equations are converted into an ordinary differential system using similarity transformations, and the numerical Keller Box scheme is applied for solutions.
MICROSYSTEM TECHNOLOGIES-MICRO-AND NANOSYSTEMS-INFORMATION STORAGE AND PROCESSING SYSTEMS
(2023)
Article
Physics, Applied
Yaya Wang, Wei Gao, Haci Mehmet Baskonus
Summary: This paper focuses on the application of the fractional natural decomposition method (FNDM) to solve the Richards equation, which describes water transport in unsaturated porous media. The effectiveness of the scheme is demonstrated through two cases with time-fractional problems, showing that the projected algorithm is easy to implement and effective in examining the behavior of nonlinear models. The reliable algorithm used in this paper can generate easily computable solutions in the form of rapidly convergent series.
MODERN PHYSICS LETTERS B
(2023)
Article
Mathematics, Applied
Ahmet Ocak Akdemir, Sinan Aslan, Mustafa Ali Dokuyucu, Ercan Celik
Summary: This study recalls the modification of the concept of exponentially convex function, a general version of convex functions given on the coordinates. By using an integral identity that involves the Riemann-Liouville (RL) fractional integral operator, new Hadamard-type inequalities are proven for exponentially convex functions on the coordinates. Many special cases of the results are discussed.
JOURNAL OF FUNCTION SPACES
(2023)
Article
Computer Science, Interdisciplinary Applications
Muhammad Umar, Zulqurnain Sabir, Muhammad Asif Zahoor Raja, Haci Mehmet Baskonus, Mohamed R. Ali, Nehad Ali Shah
Summary: This study proposes a nonlinear system for hepatitis B virus infection using the artificial neural network (ANN) combined with the genetic algorithm (GA) and sequential quadratic programming scheme (SQPS), referred to as ANN-GA-SQPS. An error function is designed based on the mathematical form of the hepatitis B virus differential model and its initial conditions. The hybrid efficiency of GA-SQPS is used to optimize the error function for the disease model, resulting in good measures of absolute error. Statistical measures are also performed to assess the constancy, reliability, and effectiveness of ANN-GA-SQPS using different indices in 50 independent executions and 30 variables.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2023)
Article
Surgery
Harun Gur, Onur Ismi, Yusuf Vayisoglu, Kemal Gorur, Murat Unal, Onurhan Guven, Cengiz Ozcan
Summary: This study retrospectively analyzed the demographic, clinical, surgical, and histopathological results and complications of 301 parotidectomies performed in southern part of Turkey. The study found that patients with malignant tumors had a higher mean age compared to patients with benign diseases. The mean age of Warthin tumor (WT) patients was significantly higher than pleomorphic adenoma (PA) patients. There was a significant male dominancy in WT compared to PA. The mean size of malignant tumors was significantly larger than benign tumors.
INDIAN JOURNAL OF OTOLARYNGOLOGY AND HEAD & NECK SURGERY
(2023)
Article
Multidisciplinary Sciences
Fei Li, Haci Mehmet Baskonus, Carlo Cattani, Wei Gao
Summary: The current study aims to provide a fundamental understanding of dynamical systems and validate the chaotic behavior of the LH equations by using the Adams-Bashforth numerical method. The LH equations are utilized to describe the chaotic laser in 4D, and the numerical solutions are obtained with different orders under different initial conditions. The classical model introduces parameter bifurcation, and the uniqueness and existence of the system are confirmed using the fixed-point hypothesis with the Caputo-Fabrizio fractional operator, followed by boundedness and dynamical analysis.
ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING
(2023)
Article
Multidisciplinary Sciences
Zulqurnain Sabir, Muhammad Asif Zahoor Raja, Haci Mehmet Baskonus, Armando Ciancio
Summary: The current study presents a mathematical model for the coronavirus, considering the effects of vaccination and quarantine. A numerical stochastic process based on L-MBNNs is used to solve the model. The model represents the dynamics of the human population, divided into subgroups of susceptible, exposed, and infected individuals, as well as quarantined, recovered/deceased, and immunized individuals. The correctness of the L-MBNNs is tested by comparing with the reference solutions using statistical methods.
ATTI ACCADEMIA PELORITANA DEI PERICOLANTI-CLASSE DI SCIENZE FISICHE MATEMATICHE E NATURALI
(2023)
Article
Engineering, Multidisciplinary
Li Yan, Zulqurnain Sabir, Esin Ilhan, Muhammad Asif Zahoor Raja, Wei Gao, Haci Mehmet Baskonus
Summary: This study presents a computational heuristic design based on the nonlinear Lienard model, using the efficiency of artificial neural networks (ANNs) and the hybridization procedures of global and local search approaches. The designed procedures of ANNs along with GA-SQPS are applied for three highly nonlinear differential models. The outcomes of the designed procedures are compared to verify their correctness, viability and efficacy.
CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES
(2023)
Article
Engineering, Multidisciplinary
Wei Gao, P. Veeresha, Haci Mehmet Baskonus
Summary: The motivation of this work is to analyze the complex nature of nonlinear models with generalized tools associated with material and history-based properties. Using a well-known numerical scheme, this study investigates the stimulating behaviors of the financial system. The impact of parameters on various financial factors and the consequences of generalizing the model within arbitrary order are discussed. The existence of a solution for the studied system is presented. This study is important for beginner researchers to examine real-world problems and predict their consequences accurately.
APPLIED MATHEMATICS IN SCIENCE AND ENGINEERING
(2023)
Article
Physics, Mathematical
Wei Gao, Haci Mehmet Baskonus
Summary: In this manuscript, the application of the rational sine-Gordon expansion method (SGEM) is focused on, and new exact solutions for the Riemann wave system and the nonlinear Gross-Pitaevskii equation (GPE) are extracted. This method utilizes the general properties of SGEM and trigonometric functions, and successfully extracts various novel analytical solutions. The physical meanings of the solutions are simulated using 2D and 3D figures and contour graphs, and the existence conditions are reported in detail. Furthermore, a detailed modulation instability analysis of the nonlinear GPE is conducted.
ADVANCES IN MATHEMATICAL PHYSICS
(2023)
