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, Interdisciplinary Applications
Q. Wei, S. Yang, H. W. Zhou, S. Q. Zhang, X. N. Li, W. Hou
Summary: This study proposes new fractional diffusion models to describe radionuclide anomalous transport in geological repository systems, and determines model parameters through fitting analysis of experimental data, showing that the proposed models are more effective in characterizing radionuclide migration. The comparison of the proposed ABFD and CFFD models is also discussed, highlighting the flexibility and accuracy of the fractional diffusion models in this study.
CHAOS SOLITONS & FRACTALS
(2021)
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
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
Engineering, Multidisciplinary
Kashif Ali Abro, Ilyas Khan, Kottakkaran Sooppy Nisar, Abdon Atangana
Summary: This paper proposes the mathematical modeling of electrochemical double layer capacitors and derives the governing equations and transfer functions through fractional differential operators. The results suggest that electrochemical double layer capacitors have higher energy storage capacities and stability compared to conventional capacitors.
ALEXANDRIA ENGINEERING JOURNAL
(2021)
Article
Mathematics, Applied
Mehmet Yavuz, Tukur Abdulkadir Sulaiman, Fuat Usta, Hasan Bulut
Summary: This study examines the existence and uniqueness of solutions to the fractional damped generalized regularized long-wave equation using the fixed-point theorem in the Atangana-Baleanu fractional derivative. The modified Laplace decomposition method is utilized to obtain approximate-analytical solutions for the nonlinear model, while numerical simulations are performed with different values of the fractional parameter to observe the effects of various parameters and variables on displacement.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematics, Interdisciplinary Applications
Xiaozhong Liao, Yong Wang, Donghui Yu, Da Lin, Manjie Ran, Pengbo Ruan
Summary: This study uses Caputo-Fabrizio and Atangana-Baleanu fractional derivatives to model the fractional order Buck-Boost converter in the time domain, and calculates the mean values of output voltage and inductor current. The results indicate that Caputo-Fabrizio and Atangana-Baleanu fractional derivatives can be applied to the Buck-Boost converter to increase the design degree of freedom, providing more choices for describing the nonlinear characteristics of the system.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Materials Science, Multidisciplinary
Asif Khan, Amir Ali, Shabir Ahmad, Sayed Saifullah, Kamsing Nonlaopon, Ali Akgul
Summary: In this article, the behaviour of the time fractional nonlinear Schrodinger equation under two different operators are investigated. Numerical and analytical solutions are obtained using the modified double Laplace transform. The error analysis shows that the system depends primarily on time, with small errors observed for small time values. The efficiency of the proposed scheme is verified with examples and further analyzed graphically and numerically.
RESULTS IN PHYSICS
(2022)
Article
Mathematics, Applied
E. Bonyah, C. W. Chukwu, M. L. Juga, Fatmawati
Summary: The article presents a mathematical model of syphilis with a focus on treatment using Caputo-Fabrizio and Atangana-Baleanu derivatives. It determines the basic reproduction number of the model and analyzes the steady states and stability of disease-free state. The study also establishes the existence and uniqueness of solutions for both types of derivatives and highlights the influence of fractional-order derivatives on the dynamics of syphilis spread.
Article
Mathematics, Interdisciplinary Applications
Joshua Kiddy K. Asamoah, Eric Okyere, Ernest Yankson, Alex Akwasi Opoku, Agnes Adom-Konadu, Edward Acheampong, Yarhands Dissou Arthur
Summary: The purpose of this study is to analyze the transmission dynamics of Q fever in livestock and ticks and to propose management practices to minimize the spread of the disease. The study develops a mathematical model to represent the spread of the disease and investigates various factors such as environmental transmission, shedding rate, and bacterial decay rate. The study also considers the memory aspect of ticks on their host by introducing fractional differential operators. The findings highlight the importance of environmental transmission and shed light on the susceptibilities and infections associated with different fractional operators.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Applied
Shabir Ahmad, Aman Ullah, Kamal Shah, Ali Akgul
Summary: This article investigates fractional dispersive partial differential equations under non-singular and non-local kernels. The Laplace transform is used to obtain the series solution of the equations, and examples are provided to confirm the validity of the proposed scheme.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics, Interdisciplinary Applications
Ya Jun Yu, Zi Chen Deng
Summary: This study establishes a unified fractional thermoelastic model for piezoelectric structures and investigates the influence of different definitions on transient responses. Theoretical and numerical methods are used to reveal the impact of fractional heat conduction laws on material properties and study the transient responses of piezoelectric materials under thermal shock.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2021)
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
Physics, Multidisciplinary
Mubashir Qayyum, Efaza Ahmad, Syed Tauseef Saeed, Hijaz Ahmad, Sameh Askar
Summary: This study focuses on a non-linear (2+1)-dimensional time-fractional Wu-Zhang (WZ) system, which is important for capturing the propagation of long waves in the ocean. The combination of the modified homotopy perturbation method (HPM) with the Laplace transform is used for solution purposes and compared with other methods. The results show that the proposed methodology is reliable and suitable for higher dimensional fractional systems.
FRONTIERS IN PHYSICS
(2023)
Article
Mathematics, Applied
Ravi Kanth Adivi Sri Venkata, Aruna Kirubanandam, Raghavendar Kondooru
Summary: In this paper, the seventh-order time-fractional Sawada Kotera Ito equation was studied using the natural transform decomposition method (NTDM) with singular and nonsingular kernel derivatives. Fractional derivatives in Caputo, Caputo-Fabrizio (CF), and Atangana-Baleanu-Caputo (ABC) were considered. The method was validated by using a few examples and comparison with actual results, showing numerical results in accordance with existing results.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Physics, Applied
Hanumesh Vaidya, Rajashekhar Choudhari, Dumitru Baleanu, K. Prasad, Shivaleela, M. Ijaz Khan, Kamel Guedri, Mohammed Jameel, Ahmed M. Galal
Summary: This study investigates phenomena such as electro-osmosis, peristalsis, and heat transfer and proposes the possibility of constructing biomimetic thermal pumping systems. A mathematical model is developed to examine the mechanisms of magnetohydrodynamics non-Newtonian flow. The findings suggest that electro-osmosis may improve peristaltic flow.
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
(2023)
Article
Physics, Applied
Rajashekhar Choudhari, Dumitru Baleanu, Hanumesh Vaidya, K. V. Prasad, M. Ijaz Khan, Omar T. Bafakeeh, Mowffaq Oreijah, Kamel Guedri, Ahmed M. Galal
Summary: The paper focuses on modeling the MHD peristaltic flow of Phan-Thien-Tanner nanofluid in an asymmetric channel with multiple slip effects. By using approximations based on long wavelength and low Reynolds number, the governing partial differential equations are transformed into nonlinear and coupled differential equations. Exact solutions for temperature and nanoparticle concentration distribution are obtained, while a perturbation technique is used to solve the nonlinear velocity distribution. Graphical analysis demonstrates the effects of essential parameters on various flow phenomena, which are crucial for understanding blood rheology.
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
(2023)
Article
Mathematics, Interdisciplinary Applications
Hasib Khan, Jehad Alzabut, Anwar Shah, Zai-yin He, Sina Etemad, Shahram Rezapour, Akbar Zada
Summary: Waterborne diseases caused by pathogenic bacteria in water pose a threat to human health. Mathematical modeling and analysis of these diseases are essential for researchers worldwide. In this paper, a waterborne disease model is transformed into a fractal-fractional integral form for qualitative analysis, with the use of an iterative convergent sequence and fixed-point technique to determine the existence of solutions. Numerical algorithms based on Lagrange's interpolation are developed for computational purposes. The effectiveness of this approach is demonstrated through a case study, providing interesting outcomes.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2023)
Article
Engineering, Electrical & Electronic
Farah Aini Abdullah, Md Tarikul Islam, J. F. Gomez-Aguilar, Md Ali Akbar
Summary: The study explores the relationship between the nonlinear coupled Konno-Oono model and the magnetic field and emphasizes the importance of solitary wave solutions for understanding relevant physical characteristics. The adoption of rational (G'/G)-expansion and improved tanh techniques successfully generates numerous wave solutions. The graphical representation of the constructed solutions reveals various solitons and clarifies their mathematical and physical significance. The competency of the adopted techniques fascinates researchers for further utilization in extracting nonlinear models.
OPTICAL AND QUANTUM ELECTRONICS
(2023)
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
Mathematical & Computational Biology
Fengsheng Chien, Hassan Saberi Nik, Mohammad Shirazian, J. F. Gomez-Aguilar
Summary: This paper investigates the stability analysis of an SEIRV model with nonlinear incidence rates and discusses the significance of control factors in disease transmission. The use of Volterra-Lyapunov matrices enables the study of global stability at the endemic equilibrium point. Additionally, an optimal control strategy is proposed to prevent the spread of coronavirus, aiming to minimize the number of infected and exposed individuals as well as treatment costs. Numerical simulations are conducted to further examine the analytical findings.
INTERNATIONAL JOURNAL OF BIOMATHEMATICS
(2024)
Article
Multidisciplinary Sciences
Hari Mohan Srivastava, Pshtiwan Othman Mohammed, Juan Luis G. Guirao, Dumitru Baleanu, Eman Al-Sarairah, Rashid Jan
Summary: The class of symmetric function interacts extensively with other types of functions, particularly with the class of positivity of functions. In this study, we propose a positive analysis technique to analyze a specific class of Liouville-Caputo difference equations of fractional-order with extremal conditions. By utilizing difference conditions, we derive relative minimum and maximum through monotonicity results. The obtained monotonicity results are verified by solving two numerical examples.
Article
Materials Science, Multidisciplinary
Behzad Ghanbari, Dumitru Baleanu
Summary: Finding optical soliton solutions to nonlinear PDEs has become a popular topic. This study aims to identify diverse wave solutions to a generalized version of the nonlinear Schrodinger equation. Two modifications to the exponential rational function method are investigated. The results show that both techniques are efficient and easy to follow, and can determine wave solutions of various PDEs.
RESULTS IN PHYSICS
(2023)
Article
Computer Science, Interdisciplinary Applications
Shah Hussain, Osman Tunc, Ghaus Ur Rahman, Hasib Khan, Elissa Nadia
Summary: This article presents a stochastic version of the epidemic model for MERS-Cov, exploring the dynamics of the disease and investigating factors that affect its spread and extinction. The study includes the analysis of global solutions, the formulation of appropriate Lyapunov functionals, and the identification of essential parameters. Graphical illustrations are provided for better understanding.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2023)
Article
Mathematics, Applied
Benoumran Telli, Mohammed Said Souid, Jehad Alzabut, Hasib Khan
Summary: This study establishes the existence and stability of solutions for a general class of Riemann-Liouville (RL) fractional differential equations (FDEs) with a variable order and finite delay, confirming the findings with fixed-point theorems (FPTs) from available literature. The RL FDE of variable order is transformed to alternate RL fractional integral structure, and classical FPTs are used to study existence results and establish Hyers-Ulam stability with the help of standard notions. The approach is broad-based and can be applied to other issues as well.
Article
Physics, Multidisciplinary
Sujoy Devnath, M. Ali Akbar, J. F. Gomez-Aguilar
Summary: This study investigates the inclusive optical soliton solutions to the (2+1)-dimensional nonlinear time-fractional Zoomeron equation and the space-time fractional nonlinear Chen-Lee-Liu equation using the extended Kudryashov technique. The obtained solutions yield a variety of typical soliton shapes and the precision of the acquired solutions is confirmed by reintroducing them into the original equation using Mathematica. This approach could introduce novel ways for unraveling other nonlinear equations and have implications in diverse sectors of nonlinear science and engineering.
Article
Computer Science, Information Systems
J. E. Lavin-Delgado, J. F. Gomez-Aguilar, D. E. Urueta-Hinojosa, Z. Zamudio-Beltran, J. A. Alanis-Navarro
Summary: In this research, a fractional-order technique for corner detection and image matching based on the Harris-Stephens algorithm and the Caputo-Fabrizio and Atangana-Baleanu derivatives is proposed and experimentally tested. The proposed technique improves image fidelity and corner extraction accuracy by designing a fractional Gaussian filter and generalizing the image derivatives using the Caputo-Fabrizio derivative. It is compared with existing methods and validated through experimental results.
MULTIMEDIA TOOLS AND APPLICATIONS
(2023)
Article
Mathematics, Applied
Velusamy Kavitha, Mani Mallika Arjunan, Dumitru Baleanu, Jeyakumar Grayna
Summary: The main motivation of this paper is to study weighted pseudo almost automorphic (WPAA) functions and establish existence results of piecewise continuous mild solution for fractional order integro-differential equations with instantaneous impulses. Traditional WPAA functions may not work due to possible discontinuity in solutions of impulsive differential equations, hence a broader concept is introduced. Main results are established using the Banach contraction mapping principle and Sadovskii's fixed point theorem. An example is presented to illustrate the analytical findings.
ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA
(2023)
Article
Engineering, Multidisciplinary
Sanjay Bhatter, Kamlesh Jangid, Shyamsunder Kumawat, Dumitru Baleanu, D. L. Suthar, Sunil Dutt Purohit
Summary: This article introduces and studies the Fredholm-type integral equation with an incomplete I-function and an incomplete I-bar-function in its kernel. The authors solve an integral problem involving IIF using fractional calculus and the Mellin transform principle. They then use the idea of the Mellin transform and fractional calculus to analyze an integral equation using the incomplete I-bar-function. Several important exceptional cases are discovered and investigated. The general discoveries in this article may lead to new integral equations and solutions that can help solve various real-world problems.
APPLIED MATHEMATICS IN SCIENCE AND ENGINEERING
(2023)
Article
Physics, Multidisciplinary
Hessah Alqahtani, Qaisar Badshah, Shazia Sakhi, Ghaus Ur Rahman, J. F. Gomez-Aguilar
Summary: This paper thoroughly examines the deterministic and stochastic models for MERS infection inside hosts. Our understanding of the dynamics of the disease and its potential for epidemic transmission is improved by studying the reproduction number and stability analysis. The combination of analytical and numerical approaches contributes to a more comprehensive assessment of MERS-CoV and aids in informing public health interventions and control strategies.
