Article
Mathematics, Interdisciplinary Applications
Mounirah Areshi, Aly R. Seadawy, Asghar Ali, Amal F. Alharbi, Abdulrahman F. Aljohani
Summary: This article investigates wave solutions of the Predator-Prey model with fractional derivative order using three modified mathematical methods. The derived solutions take the form of different functions such as trigonometric, hyperbolic, exponential, and rational functional. Some solutions are plotted in 2-dimensional and 3-dimensional by inserting specific values to attached parameters under sufficient condition on each solution for the physical phenomena of the fractional model. The proposed schemes are excellent mathematical tools for reviewing wave solutions of several fractional models in nonlinear science.
FRACTAL AND FRACTIONAL
(2023)
Article
Mathematics, Applied
Salih Djilali, Behzad Ghanbari
Summary: This research explores the influence of an infectious disease on the evolution of ecological species using a computational predator-prey model of fractional order. It is found that predators exhibit cooperative hunting behavior, and the transmission rate of the infection affects the evolution of predator-prey interactions. Graphical representations of the mathematical results are provided through a precise numerical scheme.
ADVANCES IN DIFFERENCE EQUATIONS
(2021)
Article
Mathematical & Computational Biology
Seval Isik, Figen Kangalgil
Summary: In this paper, the dynamical behaviors of a discrete-time fractional-order population model are investigated. The stability analysis and topological classification of the model at the fixed point are studied. It is shown that the model undergoes flip and Neimark-Sacker bifurcations around the co-existence fixed point. Chaos occurs when the parameter changes at the critical point. The OGY feedback method is used to control chaotic behavior resulting from Neimark-Sacker bifurcation. Numerical simulations support the analytical results, demonstrating the existence of chaotic behavior in the considered model.
INTERNATIONAL JOURNAL OF BIOMATHEMATICS
(2023)
Article
Mathematics, Interdisciplinary Applications
Boukabcha Brahim, Abdelkader Benali, Ali Hakem, Salih Djilali, Anwar Zeb, Zareen A. Khan
Summary: The effect of harvesting on predator-prey interaction and competition among predators in the case of prey herd behavior is studied using a fractional-order model. The results show the local stability of the equilibria and the effect of memory rate and harvesting on the asymptotic behavior of the solution.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2022)
Article
Mathematics
Hao Qi, Wencai Zhao
Summary: This study investigates the stability and bifurcation problems of a fractional food chain system with two kinds of delays. The nonnegative, bounded, and unique properties of the system solutions are proven. The stability of equilibrium points and the critical values of Hopf bifurcation are analyzed. The numerical simulation validates the theoretical results.
JOURNAL OF MATHEMATICS
(2022)
Article
Mathematics, Applied
Chandrali Baishya, Sindhu J. Achar, P. Veeresha, D. G. Prakasha
Summary: In this study, a fractional-order model is developed to depict the spread of infection from prey to predator. The dynamics of the model in terms of boundedness, uniqueness, and existence of solutions are surveyed. Threshold parameters are introduced to analyze equilibrium points and stability conditions, investigating global stability of various points. The novelty lies in the incorporation of fractional derivative and multiple infection pathways in the system.
Review
Engineering, Multidisciplinary
H. I. Abdel-Gawad, M. Tantawy, Abdelazeem M. Abdelwahab
Summary: This article investigates the solutions of fractional differential equations by constructing systems with fractional time derivative and fractional space derivative. The reversible identity and construction of fractional exponential function are introduced, which leads to the construction of trigonometric and hyperbolic functions. Exact solutions for linear fractional systems are obtained. In addition, an approximate analytic solution approach is presented and the convergence theorem is proved. A novel double kernel fractional derivative is introduced, with the Hilfer fractional derivative being established as a particular case. (c) 2023 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).
ALEXANDRIA ENGINEERING JOURNAL
(2023)
Article
Engineering, Multidisciplinary
Kamal Shah, Thabet Abdeljawad, Fahd Jarad, Qasem Al-Mdallal
Summary: This article studies a nonlinear fractional order Lotka-Volterra prey-predator type dynamical system using the conformable fractional order derivative (CFOD). The existence and uniqueness of at least one solution for the system are investigated using Schauder and Banach fixed point theorems. An algorithm for the approximate analytical solution is established using the conformable fractional differential transform (CFDT) technique. The results are simulated and compared with those obtained using the perturbation method for the Caputo fractional order derivative.
CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES
(2023)
Article
Mathematics, Interdisciplinary Applications
Sadiq Al-Nassir
Summary: This paper investigates the dynamics behavior of a fractional-order prey-predator system and its discretization with harvesting, considering logistic growth of prey species and Holling type III functional response. The existence and local stability of all equilibria, as well as their discretization, are determined and analyzed. The discrete model is extended to an optimal control problem for obtaining an optimal harvesting policy, with numerical simulations illustrating the theoretical findings.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Interdisciplinary Applications
Fatma Bozkurt Yousef, Ali Yousef, Chandan Maji
Summary: In this study, a fractional-order predator-prey system with fear effect was formulated to investigate the influence of fear produced by predators on the reproduction and death rates of prey population. Analysis was conducted on the existence, uniqueness, non-negativity, and boundedness of model solutions, as well as on different equilibria and their stability criteria. The study also explored the impact of fractional-order derivative and performed numerical simulations to validate the findings.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Engineering, Mechanical
Chandan Maji
Summary: This paper discusses the impact of fear on a fractional-order predator-prey model with Holling type II functional response and a constant prey refuge. The analysis includes existence, uniqueness, nonnegativity and boundedness of solutions, as well as conditions for different equilibrium points and local and global stability. It is observed that the system experiences Hopf-bifurcation around the interior equilibrium point with respect to the fractional-order derivative and refuge parameter. Numerical simulations are conducted to validate the theoretical findings.
NONLINEAR DYNAMICS
(2022)
Article
Materials Science, Multidisciplinary
H. Jafari, R. M. Ganji, N. S. Nkomo, Y. P. Lv
Summary: In this paper, the population dynamics model is generalized using Caputo-Fabrizio derivative, and a numerical scheme is presented to obtain numerical solutions of these fractional models using Adams-Bashforth scheme. The efficiency and accuracy of the scheme are shown through numerical simulations of examples.
RESULTS IN PHYSICS
(2021)
Article
Mathematics, Applied
Salih Djilali, Behzad Ghanbari
Summary: The study discusses a predator-prey interaction model involving two competitive predators and one prey, examining the existence and stability of equilibria in this complex dynamic system, as well as the influence of memory measured by fractional time derivative on temporal behavior. The mathematical results are numerically tested using a proper numerical scheme incorporating the Caputo fractional-derivative operator and the trapezoidal product-integration rule.
ADVANCES IN DIFFERENCE EQUATIONS
(2021)
Article
Mathematics, Applied
Mahmoud Moustafa, Mohd Hafiz Mohd, Ahmad Izani Ismail, Farah Aini Abdullah
Summary: This paper investigates a fractional order eco-epidemiological model with nonlinear incidence rate, dividing populations into healthy prey, infected prey, and predator, introducing a prey refuge in the healthy prey population. Various qualitative properties, including local and global stability analysis of equilibrium points, are explored. Numerical simulations confirm the theoretical results, demonstrating rich dynamical behavior in the fractional order model, including bistability phenomena, supercritical and subcritical Hopf bifurcations, and transcritical bifurcation.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2021)
Article
Mathematics, Interdisciplinary Applications
Bo Wang, Samaneh Sadat Sajjadi, Hadi Jahanshahi, Yeliz Karaca, Dingkun Hou, Li Pi, Wei-Feng Xia, Ayman A. Aly
Summary: Since ecological systems are history-dependent, incorporating fractional calculus and variable order derivatives can improve the simulation of these systems. However, there is a lack of studies considering ecological processes using variable-order fractional (VOF) models. This study proposes a VOF mathematical model for a predator-prey system, investigates its dynamic features, and develops a nonlinear model predictive control for the VOF system. The effectiveness and performance of the control technique are demonstrated through numerical simulations.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2022)
Article
Mathematics, Applied
Rahat Zarin, Amir Khan, Abdullahi Yusuf, Sayed Abdel-Khalek, Mustafa Inc
Summary: This article analyzes the fractional COVID-19 epidemic model with a convex incidence rate using the noninteger Caputo derivative. The existence and uniqueness of solutions, as well as local and global stability, are studied. Sensitivity analysis and numerical simulations are also conducted to investigate the impact of parameter changes on the system's dynamical behavior.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Mustafa Inc, Talat Korpinar, Zeliha Korpinar, Dumitru Baleanu, Ridvan Cem Demirkol
Summary: This paper examines the new evolution of polarized light ray by optical fiber in the pseudohyperbolic space H-0(2). It gives the characterization of the parallel transportation law associated with the geometric pseudohyperbolic phase of the light ray, defines the principle nature of electric and magnetic field along with the light ray in the pseudohyperbolic space H-0(2) by the geometric invariants, and successfully derives the optical solutions of nonlinear pseudohyperbolic Schrodinger's equations governing the propagation of electromagnetic fields using the traveling wave hypothesis approach.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Physics, Applied
A. S. Rashed, Mustafa Inc, R. Saleh
Summary: The investigation of plasma and electromagnetic wave interaction and propagation is crucial for understanding these phenomena. The three-dimensional Yu-Toda-Sasa-Fukuyama equation serves as a competent mathematical model for studying waves in plasma, electromagnetics, or fluids. By constructing an optimal system of infinitesimal symmetries, extensive and remarkably accurate solutions to the YTSFE can be discovered, which include periodic, polynomial, fractional, logarithmic, exponential, hyperbolic, exponential integral, Airy, and complex functions. These solutions are significant in comprehending how plasma and electromagnetic applications function under different boundary or initial conditions.
MODERN PHYSICS LETTERS B
(2023)
Article
Engineering, Electrical & Electronic
M. T. Darvishi, Mohammad Najafi, Somayeh Baloch Arbabi, Hadi Rezazadeh, Ahmet Bekir, Adem Cevikel
Summary: Searching for soliton solutions of nonlinear partial differential equations is an interesting and important area of research in the field of nonlinear phenomena. In this work, two extensions of the (2+1)-dimensional Boiti-Leon-Manna-Pempinelli equation are studied, and new multiple front wave solutions are obtained using the simplified Hirota's method and the Cole-Hopf transformation method.
OPTICAL AND QUANTUM ELECTRONICS
(2023)
Article
Engineering, Electrical & Electronic
Jamilu Sabi'u, Mayssam Tarighi Shaayesteh, Ali Taheri, Hadi Rezazadeh, Mustafa Inc, Ali Akgul
Summary: This article investigates the exact solitary wave solutions of the (3 + 1) generalized nonlinear wave equation with gas bubbles. The extended auxiliary equation method is used to explore this model, which provides various solitary wave solutions ranging from exponential to trigonometric and hyperbolic wave solutions. The results demonstrate the usefulness and efficiency of the applied method for finding solitary wave solutions of partial differential equations. Additionally, Maple mathematical software is utilized to plot some of the calculated solutions in 2D and 3D, aiding in the comprehension of the physical structures of the investigated model.
OPTICAL AND QUANTUM ELECTRONICS
(2023)
Article
Materials Science, Multidisciplinary
Mohammad Safi Ullah, M. Zulfikar Harun-Or-Roshid, M. Zulfikar Ali, Hadi Rezazadeh
Summary: The Zoomeron model is applied to study various types of solitons in fluid mechanics, laser optics, and nonlinear physics. Analytical solutions to the model are derived using different schemes, including the exp(-2(q))-expansion, the generalized Kudryashov, and the generalized tanh schemes. The obtained outcomes, including kink waves, breather waves, bright soliton, dark soliton, and singular waves, provide valuable insights for further research on complicated nonlinear models.
RESULTS IN PHYSICS
(2023)
Article
Materials Science, Multidisciplinary
Hadi Rezazadeh, Amin Gholami Davodi, Dariush Gholami
Summary: In this work, we apply the (G' / G)-expansion technique to derive traveling wave solutions of the conformable version of the Schro center dot dinger-KdV equation. These solutions are obtained using the conformable derivative. We graphically represent and compare our solutions with those in the literature, and find that our solutions are new. These results contribute to a better understanding of nonlinear phenomena observed in dusty plasma.
RESULTS IN PHYSICS
(2023)
Article
Physics, Applied
K. R. Raghunatha, Y. Vinod, Mustafa Inc, Elif Nuray Yildirim
Summary: The viscoelastic effects on double diffusive oscillatory flow in a fluid-saturated porous layer are studied. A modified Darcy-Oldroyd-B model is used to characterize the non-Newtonian fluid behavior in the porous layer. Analytical solutions for the dimensionless governing equations of fluid flow are obtained, and the effects of flow parameters on temperature, concentration, velocity profiles, skin friction, and rate of heat transfer are discussed and illustrated graphically. It is found that considering the viscoelastic behavior of the fluid is crucial for accurately predicting the behavior of oscillatory flow in double diffusive fluid systems.
MODERN PHYSICS LETTERS B
(2023)
Article
Physics, Applied
Ali Rehman, Mustafa Inc, Reem Alhefthi
Summary: The aim of this research is to investigate the impact of dynamic viscosity and viscous dissipation on graphene oxide blood-based nanofluid using analytical methods. The study focuses on the increased thermal conductivity of nanofluids over regular fluids. The flow problem is modeled using basic flow equations transformed into ordinary differential equations with the help of dimensionless parameters and thermo-physical properties. The obtained results reveal the effects of various parameters on the velocity and temperature profiles, and tabular descriptions of the convergence of the fluid flow are also provided.
MODERN PHYSICS LETTERS B
(2023)
Article
Physics, Applied
Nargis Khan, Muhammad Zeeshan, M. S. Hashmi, Mustafa Inc
Summary: This study focuses on the combined influences of variable thermal conductivity, chemical reaction, and magnetohydrodynamics (MHD) on the flow of a tangent hyperbolic nanofluid flow over an exponentially stretching surface, considering a first-order velocity slip condition. The governing equations are transformed into non-dimensional differential equations and solved numerically using the shooting technique. The results highlight the significance of different fluid parameters on the velocity, temperature, and concentration profiles. The fluid velocity profile increases with the enhancement of the We and M values, while the thermal and concentration profiles are affected by Nt, Rd, Qt, and Nb.
MODERN PHYSICS LETTERS B
(2023)
Article
Physics, Multidisciplinary
Abdul Rauf Nizami, Muhammad Rafiq, Mustafa Inc, Hammad Alotaibi, Nadeem Ahmad
Summary: This study utilizes a network model to analyze the COVID-19 dynamics in Pakistan while considering diverse mitigation strategies. The findings highlight the importance of preventing the spread of the virus into central hubs and reducing social interactions within society.
EUROPEAN PHYSICAL JOURNAL PLUS
(2023)
Article
Physics, Multidisciplinary
Muhammad Naveed, Ali Raza, Atif Hasan Soori, Mustafa Inc, Muhammad Rafiq, Nauman Ahmed, Muhammad Sajid Iqbal
Summary: This manuscript presents the stability analysis of a diarrhea epidemic model with time delay. The mathematical analysis includes the study of equilibria, positivity, boundedness, and reproduction number, as well as the sensitivity of parameters. The local and global stabilities of the model are investigated using the Routh Hurwitz criterion and Lyapunov function, respectively. Numerical results are also obtained to support the analysis.
EUROPEAN PHYSICAL JOURNAL PLUS
(2023)
Article
Materials Science, Multidisciplinary
Wafa Alfwzan, Shao-Wen Yao, F. M. Allehiany, Shabir Ahmad, Sayed Saifullah, Mustafa Inc
Summary: This study investigates the system of tsunami wave propagation along an oceanic coastline using a fractional approach. The tsunami wave system is analyzed under singular and nonsingular fractional operators. The double Laplace transform with Adomian decomposition method is used to analyze the model. The theoretical features of the considered fractional tsunami systems are explored through fixed point notions. Based on the shallow-water hypothesis, the current model is explored and it is observed that changes in sea depth and coast slope affect the tsunami wave's speed and amplification at various time scales. Numerical simulations also show that decreasing the fractional order decreases the tsunami wave velocity and height.
RESULTS IN PHYSICS
(2023)
Article
Materials Science, Multidisciplinary
Zhi-Yong Fan, Khalid K. Ali, M. Maneea, Mustafa Inc, Shao-Wen Yao
Summary: In this work, three different techniques are applied to solve the Fitzhugh-Nagumo equation, which is important for describing the propagation of electrical signals in excitable media. The methods used, including the residual power series method, homotopy perturbation method, and a modified fractional Taylor expansion, provide accurate solutions for nonlinear fractional partial differential equations. The comparison between exact and approximate solutions demonstrates the efficiency and high accuracy of these methods. Various 2D and 3D graphs are shown to support the analysis.
RESULTS IN PHYSICS
(2023)
Article
Physics, Multidisciplinary
R. K. Alhefthi, J. C. Umavathi, M. Inc, A. S. Oke
Summary: This paper investigates the significance of thermal radiation on an unsteady 2D magnetohydrodynamic squeezed nanofluid flow with a convectively heated surface. Various physical parameters are analyzed and important quantities are measured and elaborated. The results are consistent with previous studies.
PRAMANA-JOURNAL OF PHYSICS
(2023)
