Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 2Citation - Scopus: 2Computational Investigation of Hand Foot Mouth Disease Dynamics With Fuzziness(Tech Science Press, 2023) Dayan, Fazal; Ahmed, Nauman; Rafiq, Muhammad; Raza, Ali; Ahmad, Muhammad Ozair; Baleanu, DumitruThe first major outbreak of the severely complicated hand, foot and mouth disease (HFMD), primarily caused by enterovirus 71, was reported in Taiwan in 1998. HFMD surveillance is needed to assess the spread of HFMD. The parameters we use in mathematical models are usually classical mathematical parameters, called crisp parameters, which are taken for granted. But any biological or physical phenomenon is best explained by uncertainty. To represent a realistic situation in any mathematical model, fuzzy parameters can be very useful. Many articles have been published on how to control and prevent HFMD from the perspective of public health and statistical modeling. However, few works use fuzzy theory in building models to simulate HFMD dynamics. In this context, we examined an HFMD model with fuzzy parameters. A Non Standard Finite Difference (NSFD) scheme is developed to solve the model. The developed technique retains essential properties such as positivity and dynamic consistency. Numerical simulations are presented to support the analytical results. The convergence and consistency of the proposed method are also discussed. The proposed method converges unconditionally while the many classical methods in the literature do not possess this property. In this regard, our proposed method can be considered as a reliable tool for studying the dynamics of HFMD.Article Citation - WoS: 4Citation - Scopus: 4Computational Analysis for Computer Network Model With Fuzziness(Tech Science Press, 2023) Baleanu, Dumitru; Dayan, Fazal; Ullah, Sami; Ahmed, Nauman; Rafiq, Muhammad; Raza, Ali; Alfwzan, Wafa F.A susceptible, exposed, infectious, quarantined and recovered (SEIQR) model with fuzzy parameters is studied in this work. Fuzziness in the model arises due to the different degrees of susceptibility, exposure, infectivity, quarantine and recovery among the computers under consideration due to the different sizes, models, spare parts, the surrounding environments of these PCs and many other factors like the resistance capacity of the individual PC against the virus, etc. Each individual PC has a different degree of infectivity and resistance against infection. In this scenario, the fuzzy model has richer dynamics than its classical counterpart in epidemiology. The reproduction number of the developed model is studied and the equilibrium analysis is performed. Two different techniques are employed to solve the model numerically. Numerical simulations are performed and the obtained results are compared. Positivity and convergence are maintained by the suggested technique which are the main features of the epidemic models.Article Citation - WoS: 20Citation - Scopus: 23Redefined Extended Cubic B-Spline Functions for Numerical Solution of Time-Fractional Telegraph Equation(Tech Science Press, 2021) Abbas, Muhammad; Baleanu, Dumitru; Iqbal, Muhammad Kashif; Riaz, Muhammad Bilal; Amin, MuhammadThis work is concerned with the application of a redefined set of extended uniform cubic B-spline (RECBS) functions for the numerical treatment of time-fractional Telegraph equation. The presented technique engages finite difference formulation for discretizing the Caputo time-fractional derivatives and RECBS functions to interpolate the solution curve along the spatial grid. Stability analysis of the scheme is provided to ensure that the errors do not amplify during the execution of the numerical procedure. The derivation of uniform convergence has also been presented. Some computational experiments are executed to verify the theoretical considerations. Numerical results are compared with the existing schemes and it is concluded that the present scheme returns superior outcomes on the topic.Article Citation - WoS: 19Citation - Scopus: 20Numerical Control Measures of Stochastic Malaria Epidemic Model(Tech Science Press, 2020) Ahmadian, Ali; Raza, Ali; Baleanu, Dumitru; Ahsan, Muhammad Sarwar; Sathar, Mohammad Hasan Abdul; Rafiq, MuhammadNonlinear stochastic modeling has significant role in the all discipline of sciences. The essential control measuring features of modeling are positivity, boundedness and dynamical consistency. Unfortunately, the existing stochastic methods in literature do not restore aforesaid control measuring features, particularly for the stochastic models. Therefore, these gaps should be occupied up in literature, by constructing the control measuring features numerical method. We shall present a numerical control measures for stochastic malaria model in this manuscript. The results of the stochastic model are discussed in contrast of its equivalent deterministic model. If the basic reproduction number is less than one, then the disease will be in control while its value greater than one shows the perseverance of disease in the population. The standard numerical procedures are conditionally convergent. The propose method is competitive and preserve all the control measuring features unconditionally. It has also been concluded that the prevalence of malaria in the human population may be controlled by reducing the contact rate between mosquitoes and humans. The awareness programs run by world health organization in developing countries may overcome the spread of malaria disease.Article Citation - WoS: 2Citation - Scopus: 3Travelling Wave Solutions: a New Approach To the Analysis of Nonlinear Physical Phenomena(de Gruyter Poland Sp Z O O, 2014) Baleanu, Dumitru; Fardi, Mojtaba; Sayevand, KhosroIn this manuscript, a reliable scheme based on a general functional transformation is applied to construct the exact travelling wave solution for nonlinear differential equations. Our methodology is investigated by means of the modified homotopy analysis method which contains two convergence-control parameters. The obtained results reveal that the proposed approach is a very effective. Several illustrative examples are investigated in detail.Article Citation - WoS: 12Citation - Scopus: 14Family of Odd Point Non-Stationary Subdivision Schemes and Their Applications(Springeropen, 2019) Ullah, Zafar; Bari, Mehwish; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; Ghaffar, AbdulThe (2s-1)-point non-stationary binary subdivision schemes (SSs) for curve design are introduced for any integer s2. The Lagrange polynomials are used to construct a new family of schemes that can reproduce polynomials of degree (2s-2). The usefulness of the schemes is illustrated in the examples. Moreover, the new schemes are the non-stationary counterparts of the stationary schemes of (Daniel and Shunmugaraj in 3rd International Conference on Geometric Modeling and Imaging, pp.3-8, 2008; Hassan and Dodgson in Curve and Surface Fitting: Sant-Malo 2002, pp.199-208, 2003; Hormann and Sabin in Comput. Aided Geom. Des. 25:41-52, 2008; Mustafa et al. in Lobachevskii J. Math. 30(2):138-145, 2009; Siddiqi and Ahmad in Appl. Math. Lett. 20:707-711, 2007; Siddiqi and Rehan in Appl. Math. Comput. 216:970-982, 2010; Siddiqi and Rehan in Eur. J. Sci. Res. 32(4):553-561, 2009). Furthermore, it is concluded that the basic shapes in terms of limiting curves produced by the proposed schemes with fewer initial control points have less tendency to depart from their tangent as well as their osculating plane compared to the limiting curves produced by existing non-stationary subdivision schemes.Article Citation - WoS: 12Citation - Scopus: 17A New Class of 2m-Point Binary Non-Stationary Subdivision Schemes(Springer, 2019) Ullah, Zafar; Bari, Mehwish; Nisar, Kottakkaran Sooppy; Al-Qurashi, Maysaa M.; Baleanu, Dumitru; Ghaffar, AbdulA new class of 2m-point non-stationary subdivision schemes (SSs) is presented, including some of their important properties, such as continuity, curvature, torsion monotonicity, and convexity preservation. The multivariate analysis of subdivision schemes is extended to a class of non-stationary schemes which are asymptotically equivalent to converging stationary or non-stationary schemes. A comparison between the proposed schemes, their stationary counterparts and some existing non-stationary schemes has been depicted through examples. It is observed that the proposed SSs give better approximation and more effective results.Article Citation - WoS: 33Citation - Scopus: 37Extended Cubic B-Splines in the Numerical Solution of Time Fractional Telegraph Equation(Springer, 2019) Abbas, Muhammad; Ismail, Ahmad Izani; Ali, Norhashidah Hj M.; Baleanu, Dumitru; Akram, TayyabaA finite difference scheme based on extended cubic B-spline method for the solution of time fractional telegraph equation is presented and discussed. The Caputo fractional formula is used in the discretization of the time fractional derivative. A combination of the Caputo fractional derivative together with an extended cubic B-spline is utilized to obtain the computed solutions. The proposed scheme is shown to possess the unconditional stability property with second order convergence. Numerical results demonstrate the applicability, simplicity and the strength of the scheme in solving the time fractional telegraph equation with accuracies very close to the exact solutions.Article Citation - WoS: 11Citation - Scopus: 13On Solving Fractional Mobile/Immobile Equation(Sage Publications Ltd, 2017) Baleanu, Dumitru; Al Qurashi, Maysaa Mohamed; Pourbashash, HosseinIn this article, a numerical efficient method for fractional mobile/immobile equation is developed. The presented numerical technique is based on the compact finite difference method. The spatial and temporal derivatives are approximated based on two difference schemes of orders O(T2-alpha) and O(h(4)), respectively. The proposed method is unconditionally stable and the convergence is analyzed within Fourier analysis. Furthermore, the solvability of the compact finite difference approach is proved. The obtained results show the ability of the compact finite difference.