WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article Citation - WoS: 4Citation - Scopus: 5On the Convergence, Stability and Data Dependence Results of the Jk Iteration Process in Banach Spaces(de Gruyter Poland Sp Z O O, 2023) Saleem, Naeem; Bilal, Hazrat; Ahmad, Junaid; Ibrar, Muhammad; Jarad, Fahd; Ullah, KifayatThis article analyzes the JK iteration process with the class of mappings that are essentially endowed with a condition called condition (E). The convergence of the iteration toward a fixed point of a specific mapping satisfying the condition (E) is obtained under some possible mild assumptions. It is worth mentioning that the iteration process JK converges better toward a fixed point compared to some prominent iteration processes in the literature. This fact is confirmed by a numerical example. Furthermore, it has been shown that the iterative scheme JK is stable in the setting of generalized contraction. The data dependence result is also established. Our results are new in the iteration theory and extend some recently announced results of the literature.Article Citation - WoS: 2Citation - Scopus: 2Standard Routine Techniques of Modeling of Tick-Borne Encephalitis(de Gruyter Poland Sp Z O O, 2020) Arooj, Aroosa; Yasmin, Nusrat; Ghaffar, Abdul; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Khan, Ilyas; Akram, SaimaTick-borne encephalitis (TBE) is a flaviviral vector-borne disease, which is spread by a tick named Ixodes persulcatus in domestic animals as well as in humans. In this article, susceptible, exposed, infected, recovered model; with no immunity after getting recovered is taken. The only possible immunity is before getting the disease (in our model). The vaccination details are also discussed in the article. Hence, SEIS (susceptible, exposed, infected and again susceptible with zero removal from the specie compartment) is used to construct a mathematical model of TBE. TBE is acute inflammation of the brain parenchyma. After becoming viral in European states and some Asian countries, especially in China, this is an emerging viral disease in Pakistan. After constructing a model, formula for the basic reproduction number R-0-like threshold has been derived by using the next-generation matrix method. The formula for R-0-like threshold is used to evaluate whether the disease is going to be outbroken in the respective area from which the specific data are taken into consideration. The main motivation behind selection of this topic is to address the unawareness of this disease specifically in Pakistan and in its neighboring countries when there persists probability for the outbreak of this disease. Some equilibrium points and their local stability is also discussed. Numerical computations and graphs are also presented to validate the results.Article Citation - WoS: 12Citation - Scopus: 14Novel Numerical Analysis for Nonlinear Advection-Reaction Systems(de Gruyter Poland Sp Z O O, 2020) Ahmed, Nauman; Baleanu, Dumitru; Alshomrani, Ali Saleh; Iqbal, Muhammad Sajid; Rehman, Muhammad Aziz-ur; Malik, Muhammad Rafiq; Shahid, Naveed; Rafiq, MuhammadIn this article, a numerical model for a Brusselator advection-reaction-diffusion (BARD) system by using an elegant numerical scheme is developed. The consistency and stability of the proposed scheme is demonstrated. Positivity preserving property of the proposed scheme is also verified. The designed scheme is compared with the two well-known existing classical schemes to validate the certain physical properties of the continuous system. A test problem is also furnished for simulations to support our claim. Prior to computations, the existence and uniqueness of solutions for more generic problems is investigated. In the underlying system, the nonlinearities depend not only on the desired solution but also on the advection term that reflects the pivotal importance of the study.