Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Book Citation - Scopus: 7Applications in Engineering, Life and Social Sciences, Part B(De Gruyter, 2019) Lopes, A.M.; Machado, J.A.T.; Baleanu, D.This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This eighth volume collects authoritative chapters covering several applications of fractional calculus in engineering, life and social sciences, including applications in signal and image analysis, and chaos. A unique, comprehensive overview of fractional calculus and its applications With authoritative contributions from the world’s leading experts Of interest to mathematicians, physicists, and engineers. © 2019 Walter de Gruyter GmbH, Berlin/Boston.Book Citation - Scopus: 22Applications in Engineering, Life and Social Sciences, Part a(De Gruyter, 2019) Lopes, A.M.; Machado, J.A.T.; Baleanu, D.This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This seventh volume collects authoritative chapters covering several applications of fractional calculus in in engineering, life, and social sciences, including applications in biology and medicine, mechanics of complex media, economy, and electrical devices. A unique, comprehensive overview of fractional calculus and its applications With authoritative contributions from the world’s leading experts Of interest to mathematicians, physicists, and engineers. © 2019 Walter de Gruyter GmbH, Berlin/Boston.Book Part Citation - Scopus: 6Relationships Between 1d and Space Fractals and Fractional Integrals and Their Applications in Physics(De Gruyter, 2019) Baleanu, D.; Nigmatullin, R.R.In this paper, the exact relationships between the averaging procedure of a smooth function over 1D-fractal sets and the fractional integral of the RL-type are found. The numerical verifications are realized for confirmation of the analytical results and the physical meaning of these obtained formulas is discussed. Besides, the generalizations of the results for a combination of fractal circuits having a discrete set of fractal dimensions were obtained. We suppose that these new results help to deeper understand the intimate links between fractals and fractional integrals of different types, especially in applications of the fractional operators in complex systems. These results can be used in different branches of the interdisciplinary physics, where the different equations describing the complex physical phenomena, and the fractional derivatives and integrals with complex-conjugated power-law exponents are used. We consider also possibilities of applications of these results in classical mechanics. Besides these exact results, in Section 3, we consider the difficulties that can arise in attempting to generalize them for 2D and 3D fractals. We suggest one approximate approach (tested numerically) that can solve these arising difficulties. © 2019 Walter de Gruyter GmbH, Berlin/Boston.Book Part Citation - Scopus: 14Fractional Differential Equations With Bio-Medical Applications(De Gruyter, 2019) Baleanu, D.; Tang, Y.; Arshad, S.In this chapter, we investigate the dynamics of fractional order models in bio-medical. First, we examine the fractional order model of HIV Infection and analyze the stability results for non-infected and infected equilibrium points. Then, we concentrate on the fractional order tumor growth model and establish a sufficient condition for existence and uniqueness of the solution of the fractional order tumor growth model. Local stability of the four equilibrium points of the model, namely the tumor free equilibrium, the dead equilibrium of type 1, the dead equilibrium of type 2 and the coexisting equilibrium is investigated by applying Matignons condition. Dynamics of the fractional order tumor model is numerically investigated by varying the fractional-order parameter and the system parameters. © 2019 Walter de Gruyter GmbH, Berlin/Boston.Book Part Citation - Scopus: 15Fractional Calculus for Modeling Unconfined Groundwater(De Gruyter, 2019) Mehdinejadiani, B.; Baleanu, D.; Jafari, H.The porous medium which groundwater flows in is heterogeneous at all scales. This complicates the simulation of groundwater flow. Fractional derivatives, because of their non-locality property, can reduce the scale effects on the parameters and, consequently, better simulate the hydrogeological processes. In this chapter a fractional governing partial differential equation on unconfined groundwater (fractional Boussinesq equation [FBE]) is derived using the fractional mass conservation law. The FBE is a generalization of the Boussinesq equation (BE) that can be used in both homogeneous and heterogeneous unconfined aquifers. Compared to the BE, the FBE includes an additional parameter which represents the heterogeneity degree of the porous medium. This parameter changes within the range of 0 to 1 in the non-linear form of the FBE. The smaller the value of the heterogeneity degree, the more heterogeneous the aquifer is, and vice versa. To investigate the applicability of the FBE to real problems in groundwater flow, a fractional Glover-Dumm equation (FGDE) was obtained using an analytical solution of the linear form of the FBE for onedimensional unsteady flow towards parallel subsurface drains. The FGDE was fitted to water table profiles observed at laboratory and field scales, and its performance was compared to that of the Glover-Dumm equation (GDE). The parameters of the FGDE and the GDE were estimated using the inverse problem method. The results indicate that one can recognize the heterogeneity degree of porous media examined according to the obtained values for the indicator of the heterogeneity degree. The FGDE and the GDE showed similar performances in homogeneous soil, while the performance of the FGDE was significantly better than that of the GDE in heterogeneous soil. In summary, the FBE can be used as a highly general differential equation governing groundwater flow in unconfined aquifers. © 2019 Walter de Gruyter GmbH, Berlin/Boston.Book Part Citation - Scopus: 1Fractional Lagrangian and Hamiltonian Mechanics With Memory(De Gruyter, 2019) Muslih, S.I.; Baleanu, D.Fractional variational principles are very important for science and engineering. Within this field of study, the fractional Lagrangian and Hamiltonian equations are challenging ones from the viewpoint of mathematics. During the last fifteen years, the field of fractional variational principles was continuously improved and developed. In this chapter, the fractional variational principles-with and without delay-will be briefly reviewed. Several illustrative examples from mechanics are presented. © 2019 Walter de Gruyter GmbH, Berlin/Boston.Book Part Citation - Scopus: 15Discrete Fractional Masks and Their Applications To Image Enhancement(De Gruyter, 2019) Baleanu, D.; Bai, Y.-R.; Wu, G.-C.Fractional differences for image enhancement are revisited and the general methodology is illustrated in this chapter. Several fractional differences are theoretically analyzed and numerically compared. The weight coefficients derived from the discrete fractional calculus are a set of conserved quantities and they are suitable for image processing. Then a discrete fractional mask is designed within the Caputo difference and the mask coefficients are given by use of the Gamma functions. In comparison with the Grünwald-Letnikov difference and Riemann-Liouville masks, the results show this novel mask’s efficiency and simplicity. © 2019 Walter de Gruyter GmbH, Berlin/Boston.Article Determination of an Impulsive Diffusion Operator From Interior Spectral Data(De Gruyter, 2020) Baleanu, D.; Khalili, Y.In the present work, the interior spectral data is used to investigate the inverse problem for a diffusion operator with an impulse on the half line. We show that the potential functions q0(x) and q1 (x) can be uniquely established by taking a set of values of the eigenfunctions at some internal point and one spectrum. © 2020 Walter de Gruyter GmbH, Berlin/Boston 2020.Article Citation - Scopus: 1A Uniqueness Result for Differential Pencils With Discontinuities From Interior Spectral Data(De Gruyter, 2018) Baleanu, D.; Khalili, Y.In this work, the interior spectral data is employed to study the inverse problem for a differential pencil with a discontinuity on the half line. By using a set of values of the eigenfunctions at some internal point and eigenvalues, we obtain the functions q0(x) and q1(x) applied in the diffusion operator. © 2018 Walter de Gruyter GmbH, Berlin/Boston.