Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Numerical Investigation of Space Fractional Order Diffusion Equation by the Chebyshev Collocation Method of the Fourth Kind and Compact Finite Difference Scheme(American Institute of Mathematical Sciences, 2021) Azari, Yaqub; Baleanu, Dumitru; Safdari, Hamid; Jafari, Hossein; Aghdam, Yones EsmaeelzadeArticle Energy Intensity in CIS Economies: Insights into Convergence with OECD Benchmarks(Savez Ekonomista Vojvodine, 2026) Baskaraagac, Nermin YasarThis study evaluates energy intensity convergence in Commonwealth of Independent States (CIS) economies in comparison to the OECD average from 2000 to 2019, utilising beta-convergence and sigma-convergence analyses based on conventional unit root analysis alongside the KSS stationarity approach, which accounts for data nonlinearities, and the Phillips-Sul club convergence procedure. The results indicate that most CIS countries did not achieve energy intensity convergence during the period under review. Furthermore, while the Phillips-Sul test classifies all studied countries, including the OECD-20, into a single convergence club, it only presents weak evidence of significant convergence. This limited convergence is likely hindered by the continued presence of Soviet-era manufacturing infrastructure in many CIS economies. From a policy perspective, the development of comprehensive economic frameworks that incorporate legal, institutional, technical, and financial reforms, supported by targeted investments in research, cutting-edge technologies, and updated standards, is essential to significantly boost energy efficiency and effectively address challenges on both the supply and demand sides.Article Citation - WoS: 5Citation - Scopus: 5Performance Evaluation of Matched Asymptotic Expansions for Fractional Differential Equations With Multi-Order(Soc Matematice Romania, 2016) Baleanu, Dumitru; Baleanu, Dumitru; Sayevand, Khosro; MatematikAn extension of the concept of the asymptotic expansions method is presented in this paper. The multi-order differential equations of fractional order are investigated and the convergence of the proposed method is proven. The reported results show that the present approach is very effective and accurate and also are in good agreement with the ones in the literature.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: 1Citation - Scopus: 1A Higher-Order Approach for Time-Fractional Generalized Burgers' Equation(World Scientific Publ Co Pte Ltd, 2023) Deswal, Komal; Kumar, Devendra; Baleanu, Dumitru; Taneja, KomalA fast higher-order scheme is established for solving inhomogeneous time-fractional generalized Burgers' equation. The time-fractional operator is taken as the modified operator with the Mittag-Leffler kernel. Through stability analysis, it has been demonstrated that the proposed numerical approach is unconditionally stable. The convergence of the numerical method is analyzed theoretically using von Neumann's method. It has been proved that the proposed numerical method is fourth-order convergent in space and second-order convergent in time in the L-2-norm. The scheme's proficiency and effectiveness are examined through two numerical experiments to validate the theoretical estimates. The tabular and graphical representations of numerical results confirm the high accuracy and versatility of the scheme.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: 11Citation - Scopus: 15Numerical Investigation of Space Fractional Order Diffusion Equation by the Chebyshev Collocation Method of the Fourth Kind and Compact Finite Difference Scheme(Amer inst Mathematical Sciences-aims, 2021) Safdari, Hamid; Azari, Yaqub; Jafari, Hossein; Baleanu, Dumitru; Aghdam, Yones EsmaeelzadeThis paper develops a numerical scheme for finding the approximate solution of space fractional order of the diffusion equation (SFODE). Firstly, the compact finite difference (CFD) with convergence order O(delta tau 2) is used for discretizing time derivative. Afterwards, the spatial fractional derivative is approximated by the Chebyshev collocation method of the fourth kind. Furthermore, time-discrete stability and convergence analysis are presented. Finally, two examples are numerically investigated by the proposed method. The examples illustrate the performance and accuracy of our method compared to existing methods presented in the literature. 1. Introduction. One of the issues which have garnered researchers' attention these days is the fractional differential equations (FDEs) and have been numerically investigated by a huge number of authors [2, 3, 8, 9, 16, 21, 23, 25, 28, 29]. Fractional calculus is involved in many applications of science and engineering such as economics, physics, optimal control, and other applications, see [10, 11, 13, 19, 22, 26, 33, 34, 35]. A case in point is the diffusion and reaction-diffusion models inArticle 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.