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
Mathematical & Computational Biology
Muhammad Nadeem, Ji-Huan He, Hamid. M. Sedighi
Summary: This paper presents the Elzaki homotopy perturbation transform scheme (EHPTS) for analyzing the approximate solution of the multi-dimensional fractional diffusion equation. The Elzaki transform (ET) is applied to obtain a recurrence relation without any assumption or restrictive variable. The homotopy perturbation scheme (HPS) produces iterations in the form of convergence series that approach the precise solution. Graphical representations in 2D plot distribution and 3D surface solution are provided. Error analysis shows that the solution derived by EHPTS is very close to the exact solution. The obtained series demonstrates that EHPTS is a simple, straightforward, and efficient tool for other problems of fractional derivatives.
MATHEMATICAL BIOSCIENCES AND ENGINEERING
(2023)
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, Applied
Saima Rashid, Khadija Tul Kubra, Khadijah M. Abualnaja
Summary: This article extensively employs the Elzaki homotopy perturbation transform method (EHPTM) to discover the approximate solutions of fractional-order heat-like equations. The suggested approach is reinforced by convergence and error analysis and is tested with illustrative examples. EHPTM is considered to be an appropriate and convenient approach for solving fractional-order time-dependent linear and nonlinear partial differential problems.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
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
Mathematics, Interdisciplinary Applications
Saima Rashid, Rehana Ashraf, Ahmet Ocak Akdemir, Manar A. Alqudah, Thabet Abdeljawad, Mohamed S. Mohamed
Summary: This manuscript evaluates a new semi-analytical method through the Elzaki Adomian decomposition method, addressing the time-fractional Fornberg-Whitham equation and proposing a general algorithm for fuzzy Caputo and AB fractional derivatives. The convergence and error analysis are reported, showing close harmony with closed form solutions, validating the effectiveness of the proposed approach.
FRACTAL AND FRACTIONAL
(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
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
Multidisciplinary Sciences
Aisha Abdullah Alderremy
Summary: This study examines the complexities of approximate long wave and modified Boussinesq equations by introducing the Atangana-Baleanu fractional derivative operator. The analytical solution of these problems is discussed using the Elzaki transform and the Adomian decomposition method, with the characteristics of surface water waves defined through a particular relationship of dispersion. The numerical and graphical results demonstrate the computational precision and straightforwardness of the proposed method in investigating and resolving fractionally coupled nonlinear phenomena.
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
Muhammed Naeem, Noufe H. Aljahdaly, Rasool Shah, Wajaree Weera
Summary: The major goal of this research is to obtain the exact solution to the time-fractional convection-reaction-diffusion equations using a new integral transform approach. The proposed method combines the Elzaki transform and the homotopy perturbation method to tackle the nonlinearity in the considered problems. Three test examples are used to demonstrate the accuracy of the proposed scheme. The method is found to be efficient, simple, and applicable to other nonlinear problems in science and engineering.
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
Multidisciplinary Sciences
Humaira Yasmin, Naveed Iqbal
Summary: This paper applies modified analytical methods to analyze one and two-dimensional nonlinear systems of coupled Burgers and Hirota-Satsuma KdV equations. The proposed problems are solved using the Atangana-Baleanu fractional derivative operator and the Elzaki transform. The results are compared to the exact solution, and the convergence of the technique is mathematically proven. The suggested techniques are shown to be effective, simple, and accurate for solving partial differential equations or systems of partial differential equations.
Article
Physics, Multidisciplinary
Lalchand Verma, Ramakanta Meher
Summary: This study develops a novel fuzzy fractional model for the human liver and utilizes ABC gH-differentiability and a fuzzy double parametric q-homotopy analysis method. Numerical experiments show that the proposed method is more accurate and superior to the generalized Mittag-Leffler function method, as it coincides with most clinical data.
EUROPEAN PHYSICAL JOURNAL PLUS
(2022)
Article
Mathematics, Interdisciplinary Applications
Kishor D. Kucche, Sagar T. Sutar
Summary: In this paper, estimations on the Atangana-Baleanu-Caputo fractional derivative at extreme points are determined, leading to comparison results. Peano's type existence results for nonlinear fractional differential equations involving Atangana-BaleanuCaputo fractional derivative are established. The acquired comparison results are then used to address the existence of local, extremal, and global solutions.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Interdisciplinary Applications
Sayed Saifullah, Amir Ali, Arshad Khan, Kamal Shah, Thabet Abdeljawad
Summary: In this paper, a new technique called Tempered Fractional J-Transform (TFJT) is developed and its application in tempered fractional calculus is studied. The accuracy and efficiency of the proposed transform is validated through numerical illustrations, and it is believed that this work can serve as a substitute for current mathematical methods.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2023)
Article
Mathematics, Interdisciplinary Applications
Ashraf Adnan Thirthar, Prabir Panja, Aziz Khan, Manar A. Alqudah, Thabet Abdeljawad
Summary: Global warming has serious impacts on predator-prey dynamics, and this study investigates the effects of memory effect and global warming on species abundance and system stability.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2023)
Article
Engineering, Electrical & Electronic
S. Duran, H. Durur, M. Yavuz, A. Yokus
Summary: The well-known Murnaghan model of the doubly dispersive equation is studied in this work using three different mathematical methods. The solutions obtained through analytical and auxiliary equation methods are different from the literature, creating a new area of discussion. The effects of material properties and predefined values on the solution function are discussed and supported by numerical results.
OPTICAL AND QUANTUM ELECTRONICS
(2023)
Article
Physics, Multidisciplinary
Hardik Joshi, Mehmet Yavuz, Stuart Townley, Brajesh Kumar Jha
Summary: This paper proposes a non-singular SIR model with the Mittag-Leffler law, using the nonlinear Beddington-DeAngelis infection rate and Holling type II treatment rate. The qualitative properties of the model are discussed, and the local and global stability are analyzed. Conditions are developed to ensure local and global asymptotic stability. Numerical simulations are provided to support the theoretical results and investigate the impact of various factors on COVID-19. The results show that measures such as face masks, social distancing, quarantine, lockdown, immigration, and effective treatment rates can significantly reduce the infected population, while limitations in treatment resources can lead to an increase in infections.
Article
Computer Science, Artificial Intelligence
Awais Younus, Muhammad Asif, Usama Atta, Tehmina Bashir, Thabet Abdeljawad
Summary: This paper introduces a generalized concept of higher-order fuzzy conformable differentiability for fuzzy-valued functions and interprets higher-order fuzzy conformable differential equations using this concept. The fuzzy conformable Laplace transform (FCLT) is proposed as an alternative method, and some potential properties of FCLT related to higher-order fuzzy conformable derivatives are established. The FCLT method is convenient for solving fuzzy conformable linear higher-order differential equations. Examples of linear second-order and linear fourth-order fuzzy conformable initial value problems with multiple solutions are given.
Article
Mathematics, Applied
A. Boutiara, Mohammed M. Matar, Thabet Abdeljawad, Fahd Jarad
Summary: This research investigates two new types of boundary value problems, including a hybrid Langevin fractional differential equation and a coupled system of hybrid Langevin differential equations with a collective fractional derivative called the psi-Caputo fractional operator. The existence and uniqueness of solutions to these equations are addressed using the Dhage fixed point theorem and the Banach fixed point theorem, respectively. Additionally, the stability of solutions within the scope of Ulam-Hyers is also considered. Two relevant examples are provided to support the reported results.
BOUNDARY VALUE PROBLEMS
(2023)
Article
Physics, Multidisciplinary
Hardik Joshi, Mehmet Yavuz
Summary: In this paper, a fractional-order coinfection model is proposed for the transmission dynamics of COVID-19 and tuberculosis. The positivity and boundedness of the proposed model are derived, and the equilibria and basic reproduction number of different sub-models are analyzed. The stability of the sub-models is discussed, and the impact of COVID-19 on tuberculosis and vice versa is analyzed. Numerical simulations are conducted to assess the effect of biological parameters on the transmission dynamics of the coinfection.
EUROPEAN PHYSICAL JOURNAL PLUS
(2023)
Article
Mathematics
Sombir Dhaniya, Anoop Kumar, Aziz Khan, Thabet Abdeljawad, Manar A. Alqudah
Summary: In this manuscript, we study a nonlinear Langevin fractional differential equation involving the Caputo-Hadamard and Caputo fractional operators, with nonperiodic and nonlocal integral boundary conditions. The presented results establish the existence, uniqueness, and Hyers-Ulam (HU) stability of the solution to the proposed equation. The main result is obtained using the Banach contraction mapping principle and Krasonoselskii's fixed point theorem. Furthermore, an application is introduced to demonstrate the validity of the findings.
JOURNAL OF MATHEMATICS
(2023)
Article
Mathematics, Interdisciplinary Applications
Shah Muhammad, Talha Anwar, Mehmet Asifa, Mehmet Yavuz
Summary: The purpose of this work is to develop a mathematical model using a new fractional modeling approach to study flow and heat transfer dynamics. The model incorporates the Prabhakar fractional operator to transform the conventional framework to a generalized one. It evaluates the thermal effectiveness of vacuum pump oil with aluminum alloy nanoparticles. The analysis considers natural convection, the ramped velocity function, Newtonian heating, and shape-dependent relations for thermal conductivity and viscosity. The numerical results show an enhancement in thermal effectiveness and reduced flow velocity as the nanoparticles' loading range increases.
FRACTAL AND FRACTIONAL
(2023)
Article
Mathematics, Interdisciplinary Applications
Mehmet Yavuz, Fatma Ozkose, Muhittin Susam, Mathiyalagan Kalidass
Summary: In this study, a new illustrative and effective modeling approach is proposed to analyze the behaviors of Hepatitis-B virus. The mathematical modeling, equilibria, stabilities, and existence-uniqueness analysis of the model are considered, and numerical simulations using the Adams-Bashforth numerical scheme are conducted. The parameter estimation method is applied to determine the model parameters, and the sensitivity analysis of R-0 is examined. The results highlight the significant impact of the order of the fractional derivative on the dynamical process of the constructed model for Hepatitis-B.
FRACTAL AND FRACTIONAL
(2023)
Article
Mathematics, Interdisciplinary Applications
Kamal Shah, Bahaaeldin Abdalla, Thabet Abdeljawad, Manar A. Alqudah
Summary: This manuscript studies a mathematical model of progressive disease of the nervous system, also known as multiple sclerosis (MS), using the concept of fractal-fractional order derivative (FFOD) in the Caputo sense. Nonlinear functional analysis is applied to prove qualitative results including existence theory, stability, and numerical analysis. Various tools, such as Banach and Krassnoselski's fixed point theorems and Hyers-Ulam (H-U) concept, are used. The modified Euler method is utilized for numerical illustration of approximate solutions.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2023)
Article
Automation & Control Systems
M. Mallika Arjunan, Thabet Abdeljawad, A. Pratap, Ali Yousef
Summary: This paper presents asymptotic stability criteria for fractional-order gene regulatory networks (FOGRNs) with impulses and time delays, and illustrates the applicability of the results through two numerical cases. The boundedness, existence, and uniqueness of the established system are discussed using mathematical functions and theories. The delay-independent asymptotic stability criteria for FOGRNs are derived using algebraic and LMI methods, well-known inequality techniques, and Lyapunov stability theory.
ASIAN JOURNAL OF CONTROL
(2023)
Article
Computer Science, Information Systems
Muhammad Rahim, Kamal Shah, Thabet Abdeljawad, Maggie Aphane, Alhanouf Alburaikan, Hamiden Abd El-Wahed Khalifa
Summary: This study explores the design of a set of averaging and geometric aggregation operators using p, q-quasirung orthopair fuzzy numbers for addressing real-life decision-making challenges.
Article
Mathematics, Interdisciplinary Applications
Pshtiwan Othman Mohammed, Dumitru Baleanu, Eman Al-Sarairah, Thabet Abdeljawad, Nejmeddine Chorfi
Summary: This study focuses on the analytical and numerical solutions of convexity analysis for fractional differences with exponential and Mittag-Leffler kernels involving negative and non-negative lower bounds. It provides a new formula for del(2) of the discrete fractional differences and examines the correlation between non-negativity/negativity of the differences and convexity of the functions. The study defines subsets and explores the relationship between negative lower bounds and convexity on a finite time set.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2023)
Article
Mathematical & Computational Biology
Hardik Joshi, Brajesh Kumar Jha, Mehmet Yavuz
Summary: In this paper, the SV1V2EIR model is constructed to reveal the impact of two-dose vaccination on COVID-19 using Caputo fractional derivative. The model is validated and sensitivity analysis is conducted. Results show that vaccine dosage, disease transmission rate, and Caputo fractional derivative have significant effects on the vaccine efficacy.
MATHEMATICAL BIOSCIENCES AND ENGINEERING
(2023)