Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 15Citation - Scopus: 26Fractional Calculus and Application of Generalized Struve Function(Springer int Publ Ag, 2016) Baleanu, Dumitru; Al Qurashi, Maysaa' Mohamed; Nisar, Kottakkaran Sooppy; Qurashi, Maysaa’ Mohamed AlA new generalization of Struve function called generalized Galue type Struve function (GTSF) is defined and the integral operators involving Appell's functions, or Horn's function in the kernel is applied on it. The obtained results are expressed in terms of the Fox-Wright function. As an application of newly defined generalized GTSF, we aim at presenting solutions of certain general families of fractional kinetic equations associated with the Galue type generalization of Struve function. The generality of the GTSF will help to find several familiar and novel fractional kinetic equations. The obtained results are general in nature and it is useful to investigate many problems in applied mathematical science.Article Citation - WoS: 40Citation - Scopus: 46The Mean Value Theorem and Taylor's Theorem for Fractional Derivatives With Mittag-Leffler Kernel(Pushpa Publishing House, 2018) Baleanu, Dumitru; Fernandez, ArranWe establish analogues of the mean value theorem and Taylor's theorem for fractional differential operators defined using a Mittag-Leffler kernel. We formulate a new model for the fractional Boussinesq equation by using this new Taylor series expansion.Article Citation - WoS: 39Citation - Scopus: 48Chaotic Attractors With Fractional Conformable Derivatives in the Liouville-Caputo Sense and Its Dynamical Behaviors(Mdpi, 2018) Baleanu, Dumitru; Tchier, Fairouz; Solis Perez, Jesus Emmanuel; Francisco Gomez-Aguilar, Jose; Gómez-Aguilar, José Francisco; Pérez, Jesús Emmanuel SolísThis paper deals with a numerical simulation of fractional conformable attractors of type Rabinovich-Fabrikant, Thomas' cyclically symmetric attractor and Newton-Leipnik. Fractional conformable and beta-conformable derivatives of Liouville-Caputo type are considered to solve the proposed systems. A numerical method based on the Adams-Moulton algorithm is employed to approximate the numerical simulations of the fractional-order conformable attractors. The results of the new type of fractional conformable and beta-conformable attractors are provided to illustrate the effectiveness of the proposed method.Article Citation - WoS: 217Citation - Scopus: 229Some Existence Results on Nonlinear Fractional Differential Equations(Royal Soc, 2013) Rezapour, Shahram; Mohammadi, Hakimeh; Baleanu, DumitruIn this paper, by using fixed-point methods, we study the existence and uniqueness of a solution for the nonlinear fractional differential equation boundary-value problem D(alpha)u(t) = f(t, u(t)) with a Riemann-Liouville fractional derivative via the different boundary-value problems u(0) = u(T), and the three-point boundary condition u(0)= beta(1)u(eta) and u(T) = beta(2)u(eta), where T > 0, t is an element of I = [0, T], 0 < alpha < 1, 0 < eta < T, 0 < beta(1) < beta(2) < 1.Article Citation - WoS: 393Citation - Scopus: 432Anomalous Diffusion Expressed Through Fractional Order Differential Operators in the Bloch-Torrey Equation(Academic Press inc Elsevier Science, 2008) Abdullah, Osama; Baleanu, Dumitru; Zhou, Xiaohong Joe; Magin, Richard L.Diffusion weighted MRI is used clinically to detect and characterize neurodegenerative, malignant and ischemic diseases. The correlation between developing pathology and localized diffusion relies on d iffusi on -weighted pulse sequences to probe biophysical models of molecular diffusion-typically exp[-(bD)]-where D is the apparent diffusion coefficient (turn (2)/s) and b depends on the specific gradient pulse sequence parameters. Several recent studies have investigated the so-called anomalous diffusion stretched exponential model-exp[-(bD)(alpha)], where alpha is a measure of tissue complexity that can be derived from fractal models of tissue structure. In this paper we propose an alternative derivation for the stretched exponential model using fractional order space and time derivatives. First, we consider the case where the spatial Laplacian in the Bloch-Torrey equation is generalized to incorporate a fractional order Brownian model of diffusivity. Second, we consider the case where the time derivative in the Bloch-Torrey equation is replaced by a Riemann-Liouville fractional order time derivative expressed in the Caputo form. Both cases revert to the classical results for integer order operations. Fractional order dynamics derived for the first case were observed to fit the signal attenuation in diffusion-weighted images obtained from Sephadex gels, human articular cartilage and human brain. Future developments of this approach may be useful for classifying anomalous diffusion in tissues with developing pathology. (c) 2007 Elsevier Inc. All rights reserved.