Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
Browse
5 results
Search Results
Article Citation - WoS: 26Citation - Scopus: 26The Geophysical Kdv Equation: Its Solitons, Complexiton, and Conservation Laws(Springer Heidelberg, 2022) Hosseini, K.; Akbulut, A.; Baleanu, D.; Salahshour, S.; Mirzazadeh, M.; Akinyemi, L.The main goal of the current paper is to analyze the impact of the Coriolis parameter on nonlinear waves by studying the geophysical KdV equation. More precisely, specific transformations are first adopted to derive one-dimensional and operator forms of the governing model. Solitons and complexiton of the geophysical KdV equation are then retrieved with the help of several well-established approaches such as the Kudryashov and Hirota methods. In the end, the new conservation theorem given by Ibragimov is formally employed to extract conservation laws of the governing model. It is shown that by increasing the Coriolis parameter, based on the selected parameter regimes, less time is needed for tending the free surface elevation to zero.Article Citation - WoS: 12Citation - Scopus: 17Dynamics of Multi-Point Singular Fifth-Order Lane-Emden System With Neuro-Evolution Heuristics(Springer Heidelberg, 2022) Ali, Mohamed R.; Fathurrochman, Irwan; Raja, Muhammad Asif Zahoor; Sadat, R.; Baleanu, Dumitru; Sabir, ZulqurnainThe objective of the presented communication is to examine and analyze the solutions of nonlinear multi-singular fifth-order Lane-Emden (LE) system for different scenarios by variation of shape factors settled on the equivalent design of the LE equations. The neuro-evolution based stochastic computing is explored for the numerical measures using the artificial neural networks (ANNs) models for the appropriate continuous mapping, while the learning of decision variables is conducted using the integrated meta-heuristic global search of genetic algorithms (GA) hybrid with the local search efficiency of active-set (AS) i.e., ANN-GA-AS scheme. The numerical approach ANN-GA-AS is applied efficiently for the fifth kind of nonlinear LE model and statistical calculations further validate the accuracy, robustness as well as convergence.Article Citation - WoS: 23Citation - Scopus: 21Numerical Solution of a New Mathematical Model for Intravenous Drug Administration(Springer Heidelberg, 2024) Shiri, Babak; Perfilieva, Irina; Baleanu, Dumitru; Alijani, ZahraWe develop and analyze a new mathematical model for intravenous drug administration and the associated diffusion process. We use interval analysis to obtain a system of weakly singular Volterra integral equations over ordinary functions. We then use the operational method based on Chebyshev polynomials for obtaining an approximate solution of the numerical form. We show that for a certain class of fuzzy number valued functions, their generalized Hukuhara derivatives can be reduced to the derivatives of ordinary real-valued functions. By using our approach, we are able to estimate numerical solutions very accurately.Article Citation - WoS: 14Citation - Scopus: 18Oscillation of Even Order Nonlinear Delay Dynamic Equations on Time Scales(Springer Heidelberg, 2013) Mert, Raziye; Peterson, Allan; Zafer, Agacik; Erbe, LynnOne of the important methods for studying the oscillation of higher order differential equations is to make a comparison with second order differential equations. The method involves using Taylor's Formula. In this paper we show how such a method can be used for a class of even order delay dynamic equations on time scales via comparison with second order dynamic inequalities. In particular, it is shown that nonexistence of an eventually positive solution of a certain second order delay dynamic inequality is sufficient for oscillation of even order dynamic equations on time scales. The arguments are based on Taylor monomials on time scales.Article Citation - WoS: 36Citation - Scopus: 38Scintillation Advantages of Lowest Order Bessel-Gaussian Beams(Springer Heidelberg, 2008) Baykal, Y.; Sermutlu, E.; Cai, Y.; Eyyuboglu, H. T.For a weak turbulence propagation environment, the scintillation index of the lowest order Bessel-Gaussian beams is formulated. Its triple and single integral versions are presented. Numerical evaluations show that at large source sizes and large width parameters, when compared at the same source size, Bessel-Gaussian beams tend to exhibit lower scintillations than the Gaussian beam scintillations. This advantage is lost however for excessively large width parameters and beyond certain propagation lengths. Large width parameters also cause rises and falls in the scintillation index of off-axis positions toward the edges of the received beam. Comparisons against the fundamental Gaussian beam are made on equal source size and equal power basis.