Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article On the Determination of the Quadratic Pencil of the Sturm-Liouville Operator With an Impulse(Pleiades Publishing Ltd, 2025) Khalili, Y.; Baleanu, D.In this work, an inverse problem for the quadratic pencil of the Sturm-Liouville operator with an impulse in the finite interval is considered. It is shown that some information on eigenfunctions at some internal point \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$b\in\left(\frac{1}{2},1\right)$$\end{document} and parts of two spectra uniquely determine the potential functions and all parameters in the boundary conditions. Moreover we prove that the potential functions on the whole interval and the parameters in the boundary conditions can be established from one spectrum and the potentials prescribed on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left(\frac{1}{2},1\right)$$\end{document}.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 - 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: 66Citation - Scopus: 63An Accurate Numerical Technique for Solving Fractional Optimal Control Problems(Editura Acad Romane, 2015) Bhrawy, A. H.; Baleanu, Dumitru; Doha, E. H.; Baleanu, D.; Ezz-Eldien, S. S.; Abdelkawy, M. A.; MatematikIn this article, we propose the shifted Legendre orthonormal polynomials for the numerical solution of the fractional optimal control problems that appear in several branches of physics and engineering. The Rayleigh-Ritz method for the necessary conditions of optimization and the operational matrix of fractional derivatives are used together with the help of the properties of the shifted Legendre orthonormal polynomials to reduce the fractional optimal control problem to solving a system of algebraic equations that greatly simplifies the problem. For confirming the efficiency and accuracy of the proposed technique, an illustrative numerical example is introduced with its approximate solution.Article Citation - Scopus: 7Inclusion Relationships for Some Subclasses of Analytic Functions Associated With Generalized Bessel Functions(Eudoxus Press, LLC, 2018) Selvakumaran, K.A.; Baleanu, Dumitru; Al-Kharsani, H.A.; Baleanu, D.; Purohit, S.D.; Nisar, K.S.; MatematikThis paper introduces new subclasses of analytic functions and investigate the inclusion properties of these subclasses using the generalized Bessel functions of the first kind. We also derive a variety of special cases and corollaries of the main results. © 2018 by Eudoxus Press, LLC. All rights reserved.Article Citation - WoS: 7Citation - Scopus: 7On the Existence and Uniqueness of Solution of a Nonlinear Fractional Differential Equations(Eudoxus Press, Llc, 2013) Darzi, R.; Baleanu, Dumitru; Mohammadzadeh, B.; Neamaty, A.; Baleanu, D.; MatematikIn this paper, we investigate the existence and uniqueness of solution for fractional boundary value problem for nonlinear fractional differential equation D-0+(alpha) u(t) = f(t,u(t)), 0 < t < 1, 2 < alpha <= 3, with the integral boundary conditions {u(0) - gamma(1) u(1) = lambda(1) integral(1)(0) g(1) (s, u(s))ds, u'(0) - gamma(2)u'(1) = lambda(2) integral(1)(0) g(2) (s, u(s))ds, u ''(0) - gamma(2)u ''(1) = 0, where D-0+(alpha) denotes Caputo derivative of order alpha. by using the fixed point theory. We apply the contraction mapping principle and Krasnoselskii's fixed point theorem to obtain some new existence and uniqueness results. Two examples are given to illustrate the main results.Article Citation - Scopus: 4The Extension of a Modified Integral Operator To a Class of Generalized Functions(Eudoxus Press, LLC, 2018) Al-Omari, S.K.Q.; Baleanu, Dumitru; Baleanu, D.; MatematikIn this paper, we investigate a class of modified G-transforms having G-functions as kernels on a generalized space of sequences. We derive certain spaces of generalized functions named as Boehmians to legitimate the existence of the described integral. The modified G-transform is partially sharing the classical transform with some general properties. An inversion formula is also discussed on the generalized sense. © 2018 by Eudoxus Press, LLC. All rights reserved.Article Citation - WoS: 32Citation - Scopus: 33Lie Symmetry Analysis and Exact Solutions of the Time Fractional Gas Dynamics Equation(Natl inst Optoelectronics, 2016) Hashemi, M. S.; Baleanu, Dumitru; Baleanu, D.; MatematikFinding the symmetries of a given fractional differential equation is a hot topic in the field of fractional differentiation and its applications. In this manuscript, the Lie symmetries of the time fractional gas dynamics (TFGD) equation are analyzed and new exact solutions are obtained.Article Citation - WoS: 121Citation - Scopus: 125On Cauchy Problems With Caputo Hadamard Fractional Derivatives(Eudoxus Press, Llc, 2016) Jarad, Fahd; Adjabi, Y.; Baleanu, Dumitru; Jarad, Fahd; Baleanu, D.; Abdeljawad, Thabet; Abdeljawad, T.; MatematikThe current work is motivated by the so-called Caputo-type modification of the Hadamard or Caputo Hadamard fractional derivative discussed in [4]. The main aim of this paper is to study Cauchy problems for a differential equation with a left Caputo Hadamard fractional derivative in spaces of continuously differentiable functions. The equivalence of this problem to a nonlinear Volterra type integral equation of the second kind is shown. On the basis of the obtained results, the existence and uniqueness of the solution to the considered Cauchy problem is proved by using Banach's fixed point theorem. Finally, two examples are provided to explain the applications of the results.