Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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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: 15Design and Numerical Analysis of Fuzzy Nonstandard Computational Methods for the Solution of Rumor Based Fuzzy Epidemic Model(Elsevier, 2022) Rafiq, Muhammad; Ahmed, Nauman; Baleanu, Dumitru; Raza, Ali; Ahmad, Muhammad Ozair; Iqbal, Muhammad; Dayan, FazalThis model extends the classical epidemic model for cyber consumerism by introducing fuzziness to the model. Fuzziness arises due to insufficient knowledge, experimental errors, operating conditions and parameters that provide inaccurate information. The concepts of confused, escapers and recovered consumers are uncertain due to the different degrees of confusion, escaping and recovery among the individuals of the cyber consumers. The differences can arise, when the cyber consumers under the consideration having distinct habits, customs and different age groups have different degrees of resistance, etc. The chance of transmission of rumors and recovery rates are considered as fuzzy numbers. A rumor-free and two rumor existing-endemic equilibrium points have been derived for the studied model. The model is then solved numerically with fuzzy forward Euler and fuzzy nonstandard finite difference (FNSFD) methods respectively. The numerical and simulation results show that the proposed FNSFD technique is an efficient and reliable tool to deal with such type of dynamical system. (c) 2022 Elsevier B.V. All rights reserved.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: 4Citation - Scopus: 4A Fourth Order Finite Difference Method for Time-Space Fractional Diffusion Equations(Global Science Press, 2018) Baleanu, Dumitru; Huang, Jianfei; Tang, Yifa; Zhao, Yue; Arshad, SadiaA finite difference method for a class of time-space fractional diffusion equations is considered. The trapezoidal formula and a fourth-order fractional compact difference scheme are, respectively, used in temporal and spatial discretisations and the method stability is studied. Theoretical estimates of the convergence in the L-2 -norm are shown to be O(tau(2) + h(4)), where tau and h are time and space mesh sizes. Numerical examples confirm theoretical results.