Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
Browse
54 results
Search Results
Article Citation - WoS: 10Citation - Scopus: 10Novel Investigation of Stochastic Fractional Differential Equations Measles Model Via the White Noise and Global Derivative Operator Depending on Mittag-Leffler Kernel(Tech Science Press, 2024) Jarad, Fahd; Rashid, SaimaBecause of the features involved with their varied kernels, differential operators relying on convolution formulations have been acknowledged as effective mathematical resources for modeling real -world issues. In this paper, we constructed a stochastic fractional framework of measles spreading mechanisms with dual medication immunization considering the exponential decay and Mittag-Leff ler kernels. In this approach, the overall population was separated into five cohorts. Furthermore, the descriptive behavior of the system was investigated, including prerequisites for the positivity of solutions, invariant domain of the solution, presence and stability of equilibrium points, and sensitivity analysis. We included a stochastic element in every cohort and employed linear growth and Lipschitz criteria to show the existence and uniqueness of solutions. Several numerical simulations for various fractional orders and randomization intensities are illustrated.Article Citation - WoS: 8Citation - Scopus: 7A Novel Fractional Dengue Transmission Model in the Presence of Wolbachia Using Stochastic Based Artificial Neural Network(Tech Science Press, 2024) Ahmed, Iftikhar; Baleanu, Dumitru; Javeed, Shumaila; Faiz, ZeshanThe purpose of this research work is to investigate the numerical solutions of the fractional dengue transmission model (FDTM) in the presence of Wolbachia using the stochastic-based Levenberg-Marquardt neural network (LM-NN) technique. The fractional dengue transmission model (FDTM) consists of 12 compartments. The human population is divided into four compartments; susceptible humans (Sh), exposed humans (Eh), infectious humans (Ih), and recovered humans (Rh). Wolbachia-infected and Wolbachia-uninfected mosquito population is also divided into four compartments: aquatic (eggs, larvae, pupae), susceptible, exposed, and infectious. We investigated three different cases of vertical transmission probability (77), namely when Wolbachia-free mosquitoes persist only (77 = 0.6), when both types of mosquitoes persist (77 = 0.8), and when Wolbachia-carrying mosquitoes persist only (77 = 1). The objective of this study is to investigate the effectiveness of Wolbachia in reducing dengue and presenting the numerical results by using the stochastic structure LM-NN approach with 10 hidden layers of neurons for three different cases of the fractional order derivatives (alpha = 0.4, 0.6, 0.8). LM-NN approach includes a training, validation, and testing procedure to minimize the mean square error (MSE) values using the reference dataset (obtained by solving the model using the Adams-Bashforth-Moulton method (ABM). The distribution of data is 80% data for training, 10% for validation, and, 10% for testing purpose) results. A comprehensive investigation is accessible to observe the competence, precision, capacity, and efficiency of the suggested LM-NN approach by executing the MSE, state transitions findings, and regression analysis. The effectiveness of the LM-NN approach for solving the FDTM is demonstrated by the overlap of the findings with trustworthy measures, which achieves a precision of up to 10-4.Article Citation - WoS: 8Citation - Scopus: 9Numerical Computational Heuristic Through Morlet Wavelet Neural Network for Solving the Dynamics of Nonlinear Sitr Covid-19(Tech Science Press, 2022) Alnahdi, Abeer S.; Jeelani, Mdi Begum; Abdelkawy, Mohamed A.; Raja, Muhammad Asif Zahoor; Baleanu, Dumitru; Hussain, Muhammad Mubashar; Sabir, ZulqurnainThe present investigations are associated with designing Morlet wavelet neural network (MWNN) for solving a class of susceptible, infected, treatment and recovered (SITR) fractal systems of COVID-19 propagation and control. The structure of an error function is accessible using the SITR differential form and its initial conditions. The optimization is performed using the MWNN together with the global as well as local search heuristics of genetic algorithm (GA) and active-set algorithm (ASA), i.e., MWNN-GA-ASA. The detail of each class of the SITR nonlinear COVID-19 system is also discussed. The obtained outcomes of the SITR system are compared with the Runge-Kutta results to check the perfection of the designed method. The statistical analysis is performed using different measures for 30 independent runs as well as 15 variables to authenticate the consistency of the proposed method. The plots of the absolute error, convergence analysis, histogram, performance measures, and boxplots are also provided to find the exactness, dependability and stability of the MWNN-GA-ASA.Article Citation - WoS: 5Citation - Scopus: 5Stochastic Epidemic Model of Covid-19 Via the Reservoir-People Transmission Network(Tech Science Press, 2022) Fahimi, Milad; Torkzadeh, Leila; Baleanu, Dumitru; Nouri, KazemThe novel Coronavirus COVID-19 emerged in Wuhan, China in December 2019. COVID-19 has rapidly spread among human populations and other mammals. The outbreak of COVID-19 has become a global challenge. Mathematical models of epidemiological systems enable studying and predicting the potential spread of disease. Modeling and predicting the evolution of COVID-19 epidemics in near real-time is a scientific challenge, this requires a deep understanding of the dynamics of pandemics and the possibility that the diffusion process can be completely random. In this paper, we develop and analyze a model to simulate the Coronavirus transmission dynamics based on Reservoir-People transmission network. When faced with a potential outbreak, decision-makers need to be able to trust mathematical models for their decision-making processes. One of the most considerable characteristics of COVID-19 is its different behaviors in various countries and regions, or even in different individuals, which can be a sign of uncertain and accidental behavior in the disease outbreak. This trait reflects the existence of the capacity of transmitting perturbations across its domains. We construct a stochastic environment because of parameters random essence and introduce a stochastic version of the Reservoir-People model. Then we prove the uniqueness and existence of the solution on the stochastic model. Moreover, the equilibria of the system are considered. Also, we establish the extinction of the disease under some suitable conditions. Finally, some numerical simulation and comparison are carried out to validate the theoretical results and the possibility of comparability of the stochastic model with the deterministic model.Article Citation - WoS: 3Citation - Scopus: 3Examination of Pine Wilt Epidemic Model Through Efficient Algorithm(Tech Science Press, 2022) Mahmoud, Emad E.; Al-Bugami, A. M.; Baleanu, Dumitru; Rafiq, Muhammad; Mohsin, Muhammad; Al Nuwairan, Muneerah; Raza, Ali; Nuwairan, Muneerah AlPine wilt is a dramatic disease that kills infected trees within a few weeks to a few months. The cause is the pathogen Pinewood Nematode. Most plant-parasitic nematodes are attached to plant roots, but pinewood nematodes are found in the tops of trees. Nematodes kill the tree by feeding the cells around the resin ducts. The modeling of a pine wilt disease is based on six compartments, including three for plants (susceptible trees, exposed trees, and infected trees) and the other for the beetles (susceptible beetles, exposed beetles, and infected beetles). The deterministic modeling, along with subpopulations, is based on Law of mass action. The stability of the model along with equilibria is studied rigorously. The authentication of analytical results is examined through well-known computer methods like Non-standard finite difference (NSFD) and the model's feasible properties (positivity, boundedness, and dynamical consistency). In the end, comparison analysis shows the effectiveness of the NSFD algorithm.Article Citation - WoS: 11Citation - Scopus: 13Image Encryption Algorithm Based on New Fractional Beta Chaotic Maps(Tech Science Press, 2022) Natiq, Hayder; Alkhayyat, Ahmed; Farhan, Alaa Kadhim; Al-Saidi, Nadia M. G.; Baleanu, Dumitru; Ibrahim, Rabha W.In this study, a new algorithm of fractional beta chaotic maps is proposed to generate chaotic sequences for image encryption. The proposed technique generates multi random sequences by shuffling the image pixel position. This technique is used to blur the pixels connecting the input and encrypted images and to increase the attack resistance. The proposed algorithm makes the encryption process sophisticated by using fractional chaotic maps, which hold the properties of pseudo-randomness. The fractional beta sequences are utilized to alter the image pixels to decryption attacks. The experimental results proved that the proposed image encryption algorithm successfully encrypted and decrypted the images with the same keys. The output findings indicate that our proposed algorithm has good entropy and low correlation coefficients. This translates to enhanced security against different attacks. A MATLAB programming tool was used to implement and assess the image quality measures. A comparison with other image encryption techniques regarding the visual inspection and signal-to-noise ratio is provided.Article Citation - WoS: 2Citation - Scopus: 2Computational Algorithms for the Analysis of Cancer Virotherapy Model(Tech Science Press, 2022) Baleanu, Dumitru; Rafiq, Muhammad; Abbas, Syed Zaheer; Siddique, Abubakar; Javed, Umer; Nazir, Zaighum; Raza, AliCancer is a common term for many diseases that can affect any part of the body. In 2020, ten million people will die due to cancer. A worldwide leading cause of death is cancer by the World Health Organization (WHO) report. Interaction of cancer cells, viral therapy, and immune response are identified in this model. Mathematical and computational modeling is an effective tool to predict the dynamics of cancer virotherapy. The cell population is categorized into three parts like uninfected cells (x), infected cells (y), virus-free cells (v), and immune cells (z). The modeling of cancer-like diseases is based on the law of mass action (the rate of change of reacting substances is directly proportional to the product of interacting substances). Positivity, boundedness, equilibria, threshold analysis, are part of deterministic modeling. Later on, a numerical analysis is designed by using the standard and non-standard finite difference methods. The non-standard finite difference method is developed to study the long-term behavior of the cancer model. For its efficiency, a comparison of the methods is investigated.Article Bio-Inspired Modelling of Disease Through Delayed Strategies(Tech Science Press, 2022) Baleanu, Dumitru; Raza, Ali; Anwar, Pervez; Ahmed, Nauman; Rafiq, Muhammad; Cheema, Tahir Nawaz; Nasir, AroojIn 2020, the reported cases were 0.12 million in the six regions to the official report of the World Health Organization (WHO). For most children infected with leprosy, 0.008629 million cases were detected under fifteen. The total infected ratio of the children population is approximately 4.4 million. Due to the COVID-19 pandemic, the awareness programs implementation has been disturbed. Leprosy disease still has a threat and puts people in danger. Nonlinear delayed modeling is critical in various allied sciences, including computational biology, computational chemistry, computational physics, and computational economics, to name a few. The time delay effect in treating leprosy delayed epidemic model is investigated. The whole population is divided into four groups: those who are susceptible, those who have been exposed, those who have been infected, and those who have been vaccinated. The local and global stability of well-known conclusions like the Routh Hurwitz criterion and the Lyapunov function has been proven. The parameters' sensitivity is also examined. The analytical analysis is supported by computer results that are presented in a variety of ways. The proposed approach in this paper preserves equilibrium points and their stabilities, the existence and uniqueness of solutions, and the computational ease of implementation.Article Citation - WoS: 4Citation - Scopus: 4Stochastic Analysis for the Dynamics of a Poliovirus Epidemic Model(Tech Science Press, 2022) Baleanu, Dumitru; Khan, Zafar Ullah; Mohsin, Muhammad; Ahmed, Nauman; Rafiq, Muhammad; Anwar, Pervez; Raza, AliMost developing countries such as Afghanistan, Pakistan, India, Bangladesh, and many more are still fighting against poliovirus. According to the World Health Organization, approximately eighteen million people have been infected with poliovirus in the last two decades. In Asia, still, some countries are suffering from the virus. The stochastic behavior of the poliovirus through the transition probabilities and non-parametric perturbation with fundamental properties are studied. Some basic properties of the deterministic model are studied, equilibria, local stability around the stead states, and reproduction number. Euler Maruyama, stochastic Euler, and stochastic Runge-Kutta study the behavior of complex stochastic differential equations. The main target of this study is to develop a nonstandard computational method that restores dynamical features like positivity, boundedness, and dynamical consistency. Unfortunately, the existing methods failed to fix the actual behavior of the disease. The comparison of the proposed approach with existing methods is investigated.Article Citation - WoS: 1Citation - Scopus: 1Stability Scrutinization of Agrawal Axisymmetric Flow of Nanofluid Through a Permeable Moving Disk Due To Renewable Solar Radiation With Smoluchowski Temperature and Maxwell Velocity Slip Boundary Conditions(Tech Science Press, 2023) Zaib, Aurang; Ishak, Anuar; Waini, Iskandar; Sherif, El-Sayed M.; Baleanu, Dumitru; Khan, UmairThe utilization of solar energy is essential to all living things since the beginning of time. In addition to being a constant source of energy, solar energy (SE) can also be used to generate heat and electricity. Recent technology enables to convert the solar energy into electricity by using thermal solar heat. Solar energy is perhaps the most easily accessible and plentiful source of sustainable energy. Copper-based nanofluid has been considered as a method to improve solar collector performance by absorbing incoming solar energy directly. The goal of this research is to explore theoretically the Agrawal axisymmetric flow induced by Cu-water nanofluid over a moving permeable disk caused by solar energy. Moreover, the impacts of Maxwell velocity and Smoluchowski temperature slip are incorporated to discuss the fine points of nanofluid flow and characteristics of heat transfer. The primary partial differential equations are transformed to similarity equations by employing similarity variables and then utilizing bvp4c to resolve the set of equations numerically. The current numerical approach can produce double solutions by providing suitable initial guesses. In addition, the results revealed that the impact of solar collector efficiency enhances significantly due to nanoparticle volume fraction. The suction parameter delays the boundary layer separation. Moreover, stability analysis is performed and is found that the upper solution is stable and physically trustworthy while the lower one is unstable.