Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
Browse
62 results
Search Results
Article Citation - Scopus: 4On Mild Solution of Abstract Neutral Fractional Order Impulsive Differential Equations With Infinite Delay(Eudoxus Press, LLC, 2018) Anguraj, A.; Baleanu, Dumitru; Kanjanadevi, S.; Baleanu, D.; MatematikWe prove the existence and uniqueness of fractional neutral impulsive differential equations with infinite delay via contraction mapping principle and fixed point technique for condensing map. We use the resolvent operator technique for integral equations to make the mild solution of the problem more appropriate. © 2018 by Eudoxus Press, LLC. All rights reserved.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 - Scopus: 2Non-Integer Variable Order Dynamic Equations on Time Scales Involving Caputo-Fabrizio Type Differential Operator(Eudoxus Press, LLC, 2018) Baleanu, D.; Baleanu, Dumitru; Nategh, M.; MatematikThis work deals with the conecept of a Caputo-Fabrizio type non-integer variable order differential opertor on time scales that involves a non-singular kernel. A measure theoretic discussion on the limit cases for the order of differentiation is presented. Then, corresponding to the fractional derivative, we discuss on an integral for constant and variable orders. Beside the obtaining solutions to some dynamic problems on time scales involving the proposed derivative, a fractional folrmulation for the viscoelastic oscillation problem is studied and its conversion into a third order dynamic equation is presented. © 2018 by Eudoxus Press, LLC. All rights reserved.Article Citation - Scopus: 1A Lebesgue Integrable Space of Boehmians for a Class of Dk Transformations(Eudoxus Press, LLC, 2018) Al-Omari, S.; Baleanu, Dumitru; Baleanu, D.; MatematikBoehmians are objects obtained by an abstract algebraic construction similar to that of field of quotients and it in some cases just gives the field of quotients. As Boehmian spaces are represented by convolution quotients, integral transforms have a natural extension onto appropriately defined spaces of Boehmians. In this paper, we have defined convolution products and a class of delta sequences and have examined the axioms necessary for generating the Dk spaces of Boehmians. The extended Dk transformation has therefore been defined as a one-to-one onto mapping continuous with respect to Δ and δ convergences. Over and above, it has been asserted that the necessary and sufficient conditions for an integrable sequence to be in the range of the Dk transformation is that the class of quotients belongs to the range of the representative. Further results related to the inverse problem are also discussed. © 2018 EUDOXUS PRESS, LLC.Article Citation - WoS: 5Citation - Scopus: 7On Some Self-Adjoint Fractional Finite Difference Equations(Eudoxus Press, Llc, 2015) Baleanu, Dumitru; Baleanu, Dumitru; Rezapour, Shahram; Salehi, Saeid; MatematikRecently, the existence of solution for the fractional self-adjoint equation Delta(nu)(nu-1) (p Delta y)(t) = h(t) for order 0 < nu <= 1 was reported in [9]. In this paper, we investigated the self-adjoint fractional finite difference equation Delta(nu)(nu-2)(p Delta u(t) = j(t,p(t+nu - 2)) via the boundary conditions y(nu - 2) = 0 , such that Delta y(nu - 2) = 0 and Delta y(nu+b) = 0. Also, we analyzed the self-adjoing fractional finite difference equation Delta(nu()(nu-2)p Delta(2)y)(t) = j(t,[(t+nu - 2)Delta(2)y(t+nu-3)) via the boundary conditions y(nu - 2) = 0, Delta y(nu - 2) = 0, Delta(2)y(nu - 2) = 0 and Delta 2y(nu+b) = 0. Finally, we conclude a result about the existence of solution for the general equation Delta(nu()(nu-2)p Delta(m)y)(t) = h(t,p(t+nu - m - 1)Delta(m)y(t+nu - m - 1)) via the boundary conditions y(nu - 2) = Delta y(nu - 2) = Delta(2)y(nu - 2) = center dot center dot center dot Delta(m)y(nu+b) = 0 for oder 1 < nu <= 2.Article Citation - WoS: 34Citation - Scopus: 30New Solutions of the Transport Equations in Porous Media Within Local Fractional Derivative(Editura Acad Romane, 2016) Zhang, Yu; Baleanu, Dumitru; Baleanu, Dumitru; Yang, Xiao-Jun; MatematikIn this manuscript we use the series expansion method within local fractional derivative to obtain the solutions of both homogeneous and non-homogeneous transport equations. The new reported solutions are able to describe more efficiently the behavior of solutions of the transport phenomena in porous media.Article Citation - WoS: 4Citation - Scopus: 6A Fractional Derivative Inclusion Problem Via an Integral Boundary Condition(Eudoxus Press, Llc, 2016) Baleanu, Dumitru; Baleanu, Dumitru; Moghaddam, Mehdi; Mohammadi, Hakimeh; Rezapour, Shahram; MatematikWe investigate the existence of solutions for the fractional differential inclusion (c)D(alpha)x(t) is an element of F(t, x(t)) (equipped with the boundary value problems x(0) = 0 and x(1) = integral(eta)(0) x(s)ds, where 0 < eta < 1, 1 < alpha <= 2, D-c(alpha) is the standard Caputo differentiation and F : [0, 1] x R -> 2(R) is a compact valued multifunction. An illustrative example is also discussed.Article Citation - WoS: 5Citation - Scopus: 6A Note on Fractional Neutral Integro-Differential Inclusions With State-Dependent Delay in Banach Spaces(Eudoxus Press, Llc, 2016) Suganya, Selvaraj; Baleanu, Dumitru; Baleanu, Dumitru; Arjunan, Mani Mallika; MatematikWe have applied different fixed point theorems to examine the existence results for fractional neutral integro-differential inclusions (FNIDI) with state-dependent delay (SDD) in Banach spaces. We tend to conjointly discuss the cases once the multivalued nonlinear term takes convex values further as nonconvex values. An example is offered to demonstrate the obtained results.Article Citation - WoS: 16Citation - Scopus: 17Fractional Synchronization of Chaotic Systems With Different Orders(Editura Acad Romane, 2012) Razminia, Abolhassan; Baleanu, Dumitru; Baleanu, Dumitru; MatematikIn this paper, we consider two chaotic systems with different orders. First, we consider the case when one of them is fractional order (master system) and another one is integer order (slave system). Second, we consider the case when both of them are fractional order but the orders are different. Using a fractional synchronization scheme in the presence of discrepancy between initial conditions of these systems for both cases the trajectories of the slave system are forced to track the master system trajectories. The effectiveness of the proposed technique is verified by numerical simulations for Chen systems.Article Citation - WoS: 4Citation - Scopus: 5One-Dimension Continuous Wavelet Resolution for the Simultaneous Analysis of Binary Mixture of Benazepril and Hydrochlorothiazide in Tablets Using Spectrophotometric Absorbance Data(Editura Academiei Romane, 2004) Dinç, E; Baleanu, Dumitru; Baleanu, D; MatematikOne-dimensional continuous wavelets transform (CWT) followed by a zero-crossing technique were applied to the quantitative resolution of a binary mixture of benazepril (BE) and hydrochlorothiazide (HCT) in two commercial tablet formulations. UV-spectra in the range of 210.1-300.0 nm, were recorded and transferred as vectors having 900 components into MATLAB 6.5. The analyzed signals corresponding to the above vectors were subjected to three CWT families, namely, Mexican (MEX), Haar (HA) and Daubechies3 (DAUB3) wavelets. For these three families a detailed analysis procedure was performed and we retained only those parameters creating many zero-crossing points for transformed signals. At locations where the wavelet transform of one component vanishes, the value of the mixture's transformed signal is due only to the other component. This allows rapid approximate determination of the concentrations. The above three wavelet bases provided reliable results of the analysis of the mixtures containing BE and HCT in two pharmaceutical tablet formulations.