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, Applied
Cuiying Li, Rui Wu, Ranzhuo Ma
Summary: This paper investigates the existence and uniqueness of solutions for nonlinear quadratic iterative equations in the sense of the Caputo fractional derivative with different boundary conditions. It demonstrates the existence and uniqueness of a solution for the boundary value problems of Caputo fractional iterative equations with arbitrary order by applying the Leray-Schauder fixed point theorem and topological degree theory. It also establishes the well posedness of the control problem of a nonlinear iteration system with a disturbance and guarantees the existence of solutions for a neural network iterative system.
Article
Engineering, Multidisciplinary
Ebraheem Alzahrani, M. M. El-Dessoky, Dumitru Baleanu
Summary: The COVID-19 pandemic, originating from Wuhan China, continues to cause panic globally, requiring adherence to guidelines set by the World Health Organization for its eradication. This study introduces a new mathematical model for COVID-19, utilizing real infection cases reported from Saudi Arabia, to analyze transmission and treatment effects on disease dynamics. The study concludes that fractional order epidemic models offer more insights into disease dynamics and are more suitable for modeling the COVID-19 outbreak.
ALEXANDRIA ENGINEERING JOURNAL
(2021)
Article
Mathematics, Interdisciplinary Applications
Kottakkaran Sooppy Nisar, Muhammad Farman, Evren Hincal, Aamir Shehzad
Summary: Smoking is considered an epidemic due to the high mortality rate and significant costs associated with it. This study focuses on utilizing the hybrid fractional differential operator to analyze the dynamics of a fractional order quitting smoking model. The research reveals that smoking is the third leading cause of death among humans and the most preventable cause of illness.
CHAOS SOLITONS & FRACTALS
(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
Physics, Multidisciplinary
P. Veeresha, Esin Ilhan, Haci Mehmet Baskonus
Summary: In this paper, the solution to coupled equations describing projectile motion with wind-influence is found using the q-homotopy analysis transform method (q-HATM). The proposed method combines q-homotopy analysis scheme and Laplace transform, while defining fractional derivative with Caputo-Fabrizio (CF) operator. The achieved consequences demonstrate that the solution procedure is easy to implement, highly systematic, and accurate in analyzing nonlinear differential equations of integer and fractional order.
Article
Computer Science, Interdisciplinary Applications
Assad Sajjad, Muhammad Farman, Ali Hasan, Kottakkaran Sooppy Nisar
Summary: This scientific study investigates the yellow virus in red chili plants using the Caputo-Fabrizio and fractal fractional derivative operators. It is important to develop methods to prevent the spread of the yellow virus in red chili plants.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2023)
Article
Mathematics, Interdisciplinary Applications
Ridhwan Reyaz, Ahmad Qushairi Mohamad, Yeou Jiann Lim, Muhammad Saqib, Sharidan Shafie
Summary: Fractional derivatives have wide applications in engineering, medical, and manufacturing sciences, and their geometrical representations in fluid flow are still being explored. This study presents an analytical solution to investigate the impact of the Caputo-Fabrizio fractional derivative on magnethohydrodynamic fluid flow with thermal radiation and chemical reaction, and numerical analysis of skin friction, Nusselt number, and Sherwood number.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics, Applied
Kamal Shah, Thabet Abdeljawad, Bahaaeldin Abdalla
Summary: In this paper, a coupled system with CaputoFabrizio derivative (CFD) under coupled integral boundary conditions is considered. The authors aim to derive necessary and sufficient conditions for the existence of at least one solution. They also propose a monotone iterative scheme combined with the upper and lower solution method to calculate extremal solutions. Perov's fixed point theorem is used to study the existing criteria for the solution, and results related to at least one solution are obtained using Schauder's fixed point theorem. Graphical presentations of upper and lower solutions are provided to illustrate the results.
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
Mathematics, Applied
Sabri T. M. Thabet, Mohammed S. Abdo, Kamal Shah
Summary: This study is devoted to the investigation of the existence and uniqueness of solutions of a mathematical model on the transmission dynamics of COVID-19, using a nonsingular kernel type derivative with fractional order and Picard's iterative method. Additionally, Laplace transform and Adomian's decomposition method were utilized to explore approximate solutions, with graphical presentations provided for different fractional orders of the model.
ADVANCES IN DIFFERENCE EQUATIONS
(2021)
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, Applied
Amr M. S. Mahdy
Summary: In this study, fractional order is applied to the glioblastoma multiforme (GBM) and IS interaction models to investigate the stability and existence of the GBM disease. The model can effectively simulate the spread of epidemics and the behavior of the model can be adjusted by changing parameters.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Khalid K. Ali, K. R. Raslan, Amira Abd-Elall Ibrahim, Mohamed S. Mohamed
Summary: In this paper, the existence, uniqueness, and continuous dependence of solutions for a coupled system of fractional q-integro-differential equations are investigated using the definitions of the Caputo-Fabrizio fractional derivative and the Riemann-Liouville fractional q-integral. An overview of the finite-trapezoidal method is provided. Finally, some numerical examples are presented to demonstrate the effectiveness of the method.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Multidisciplinary Sciences
Shajar Abbas, Zaib Un Nisa, Mudassar Nazar, Muhammad Amjad, Haider Ali, Ahmed Zubair Jan
Summary: The application of fractional derivatives in fluid flow has been explored, with experimental and theoretical research showcasing their effectiveness in unsteady boundary layers. The results demonstrate the broader applicability of fractional derivatives across various orders.
ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING
(2023)
Article
Mathematics, Applied
Sunil Dutt Purohit, Dumitru Baleanu, Kamlesh Jangid
Summary: In this article, solutions of a generalised multiorder fractional partial differential equations involving the Caputo time-fractional derivative and the Riemann-Liouville space fractional derivatives are studied using the Laplace-Fourier transform technique. The proposed equations can be reduced to the Schrodinger equation, wave equation, and diffusion equation in a more general sense. Solutions of the equation proposed in the stochastic resetting theory in the context of Brownian motion are also found in a general regime.
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
Engineering, Multidisciplinary
Pallavi S. Scindia, Kottakkaran S. Nisar
Summary: This paper investigates the stability of impulsive Volterra delay integrodifferential equations in Banach spaces, using Pachpatte's type integral inequality with integral impulses. The obtained results are supported with suitable examples.
INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION
(2023)
Article
Computer Science, Theory & Methods
Pushpendra Kumar, Vedat Suat Erturk, V Govindaraj, Mustafa Inc, Hamadjam Abboubakar, Kottakkaran Sooppy Nisar
Summary: In this paper, two different nonclassical Coronavirus models are analyzed using Caputo and Caputo-Fabrizio fractional derivatives. Graphical simulations are performed to demonstrate the behavior of these systems. The study finds that fractional-order solutions can describe disease dynamics more clearly, and the model dynamics vary under different kernel functions.
INTERNATIONAL JOURNAL OF MODELING SIMULATION AND SCIENTIFIC COMPUTING
(2023)
Article
Multidisciplinary Sciences
Dinesh Kumar, Frederic Ayant, Kottakkaran Sooppy Nisar, Daya Lal Suthar
Summary: In this article, we introduce the concepts of fractional-order Kober and generalized Weyl q-integrals, as well as present the properties and results of Riemann-Liouville and Weyl fractional q-integral transforms. By specializing variables and parameters, a wide variety of useful basic functions can be obtained.
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES INDIA SECTION A-PHYSICAL SCIENCES
(2023)
Article
Physics, Multidisciplinary
Muhammad Shoaib, Kottakkaran Sooppy Nisar, Muhammad Asif Zahoor Raja, Saba Kainat
Summary: The unsteady flow field properties of the Williamson Magneto Hydrodynamic Fluid Model are analyzed using the Bayesian regularization algorithm with a backpropagation artificial neural network. By transforming the non-linear partial differential equations of the model, ordinary differential equations are obtained. Data is generated using Matlab and the Adam numerical technique. The algorithm's performance is evaluated through mean square error results, error analysis plots, regression, and error histograms, with a mean square error validation at the level of E-13.
WAVES IN RANDOM AND COMPLEX MEDIA
(2023)
Article
Mathematics, Applied
C. Dineshkumar, R. Udhayakumar, V. Vijayakumar, Anurag Shukla, Kottakkaran Sooppy Nisar
Summary: This article primarily focuses on the approximate controllability of nonlocal Atangana-Baleanu fractional derivative by Mittag-Leffler kernel to stochastic differential systems. We obtain new sufficient conditions for the approximate controllability of nonlinear Atangana-Baleanu fractional stochastic differential inclusions under the assumption that the corresponding linear system is approximately controllable. Additionally, we establish the approximate controllability results for the Atangana-Baleanu fractional stochastic control system with infinite delay. The results are obtained using the fixed-point theorem for multivalued operators and fractional calculus. An example is included to demonstrate the applicability of the results.
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS
(2023)
Article
Mathematics, Applied
M. A. Abdelkawy, E. M. Soluma, Ibrahim Al-Dayel, Dumitru Baleanu
Summary: A numerical investigation is conducted in this paper for a class of Riesz space-fractional nonlinear wave equations (MD-RSFN-WEs). The presence of a spatial Laplacian of fractional order, described by fractional Riesz derivatives, is considered in the model. The fractional wave equation governs the mechanical diffusive wave propagation in viscoelastic medium with power-law creep and provides a physical understanding of this equation in the context of dynamic viscoelasticity. A totally spectral collocation approach is used to deal with the independent variables, and the results demonstrate that the spectral scheme is exponentially convergent.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2023)
Article
Engineering, Mechanical
Reetika Chawla, Komal Deswal, Devendra Kumar, Dumitru Baleanu
Summary: In this study, we investigated the effectiveness of three linearization approaches for solving the time-fractional generalized Burgers' equation using a modified version of the fractional derivative known as the Atangana-Baleanu Caputo derivative. A stability analysis of the linearized time-fractional Burgers' difference equation was also conducted. All linearization strategies used to solve the proposed nonlinear problem were found to be unconditionally stable. Two numerical examples were considered to support the theory. Additionally, numerical results compared the different linearization strategies and demonstrated the effectiveness of the proposed numerical scheme in three distinct ways.
JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS
(2023)
Article
Mathematics, Interdisciplinary Applications
Ausif Padder, Laila Almutairi, Sania Qureshi, Amanullah Soomro, Afroz Afroz, Evren Hincal, Asifa Tassaddiq
Summary: In this study, the Caputo fractional-order derivative is used to perform a dynamical analysis of a generalized tumor model. The results show that the Caputo fractional-order derivative provides a more accurate description of the tumor growth dynamics compared to classical integer-order derivatives. The study also highlights the potential of the Caputo fractional-order derivative as a valuable tool in biomedical research.
FRACTAL AND FRACTIONAL
(2023)
Article
Mathematics, Applied
Kottakkaran Sooppy Nisar, R. Jagatheeshwari, C. Ravichandran, P. Veeresha
Summary: This article explores the applications of reaction-diffusion models, particularly the Brusselator reaction-diffusion system (BRDS), which is known for its cross diffusion and pattern formations in biology and chemistry. The authors derive an analytical solution of the fractional Brusselator reaction-diffusion system (FBRDS) using a novel method called residual power series method (RPSM). The solution of the system has been analyzed graphically.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Physics, Multidisciplinary
Samriti Dhiman, Tanya Sharma, Kuldeep Singh, Kottakkaran S. Nisar, Rakesh Kumar, C. S. K. Raju
Summary: This study introduces the novel concept of thermal and solutal stratifications in a nanofluid's non-orthogonal stagnation point flow and solves the problem using numerical methods. The results show that solutal stratification has a greater impact on mass transfer and reduces the skin friction coefficient.
EUROPEAN PHYSICAL JOURNAL PLUS
(2023)
Article
Mathematics, Interdisciplinary Applications
Muhammad Shoaib, Ghania Zubair, Kottakkaran Sooppy Nisar, Muhammad Asif Zahoor Raja, Mohammed S. S. Alqahtani, Mohamed Abbas, H. M. Almohiy
Summary: This paper introduces a new Meyer neuro-evolutionary computational algorithm that combines the hybrid heuristics of Meyer wavelet neural network with the global optimized search efficiency of genetic algorithm and sequential quadratic programming for mathematical modeling of the epidemiological smoking model. According to the World Health Organization, tobacco consumption kills 10% of all adults worldwide. The smoking epidemic is considered the greatest health threat humanity has ever faced, making it crucial to address using the suggested hybrid techniques.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2023)
Article
Mathematics, Interdisciplinary Applications
Fazli Hadi, Rohul Amin, Ilyas Khan, J. Alzahrani, K. S. Nisar, Amnahs S. Al-Johani, Elsayed Tag Eldin
Summary: This paper numerically studies the Haar wavelet collocation method (HWCM) for solving nonlinear delay Volterra, delay Fredholm, and delay Volterra-Fredholm Integro-Differential Equations (IDEs). The HWCM technique reduces the given equations into a system of nonlinear algebraic equations, which are solved using Broydens technique. Numerical examples are used for validation and demonstrate the computational efficiency and convergence of the proposed method. The results show that the HWCM is a simple, precise, and efficient method.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2023)
Article
Computer Science, Interdisciplinary Applications
Muhammad Farman, Aqeel Ahmad, Anum Zehra, Kottakkaran Sooppy Nisar, Evren Hincal, Ali Akgul
Summary: Diabetes is a significant public health issue that affects millions of people worldwide. This study proposes a mathematical model to understand the mechanisms of glucose homeostasis, providing valuable insights for diabetes management. The model incorporates fractional operators and analyzes the impact of a new wave of dynamical transmission on equilibrium points, offering a comprehensive understanding of glucose homeostasis.
MATHEMATICS AND COMPUTERS IN SIMULATION
(2024)
