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 - WoS: 36Citation - Scopus: 41Numerical Treatment of Coupled Nonlinear Hyperbolic Klein-Gordon Equations(Editura Acad Romane, 2014) Doha, E. H.; Baleanu, Dumitru; Bhrawy, A. H.; Baleanu, D.; Abdelkawy, M. A.; MatematikA semi-analytical solution based on a Jacobi-Gauss-Lobatto collocation (J-GL-C) method is proposed and developed for the numerical solution of the spatial variable for two nonlinear coupled Klein-Gordon (KG) partial differential equations. The general Jacobi-Gauss-Lobatto points are used as collocation nodes in this approach. The main characteristic behind the J-GL-C approach is that it reduces such problems to solve a system of ordinary differential equations (SODEs) in time. This system is solved by diagonally-implicit Runge-Kutta-Nystrom scheme. Numerical results show that the proposed algorithm is efficient, accurate, and compare favorably with the analytical solutions.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: 60Citation - Scopus: 68Lyapunov-Krasovskii Stability Theorem for Fractional Systems With Delay(Editura Acad Romane, 2011) Baleanu, Dumitru; Baleanu, D.; Ranjbar N, A.; Abdeljawad, Thabet; Sadati R, S. J.; Delavari, R. H.; Abdeljawad (Maraaba), T.; Gejji, V.; MatematikFractional calculus techniques and methods started to be applied during the last decades in several fields of science and engineering. In this paper we studied the stability of fractional order nonlinear time-delay systems for Caputo's derivative and we extended Lyapunov-Krasovskii theorem for the fractional nonlinear systems.Article Citation - Scopus: 9Hamilton-Jacobi Treatment of Fields With Constraints(Editrice Compositori s.r.l., 2000) Baleanu, D.; Baleanu, Dumitru; Güler, Y.; Güler, Yurdahan; MatematikIn this paper Güler's formalism for the systems with finite degrees of freedom is applied to the field theories with constraints. The integrability conditions are investigated and the path integral quantization is performed using the action given by Hamilton-Jacobi formulation. Proca's model is investigated in details.Article Citation - Scopus: 61Solving Multi-Term Orders Fractional Differential Equations by Operational Matrices of Bps With Convergence Analysis(2013) Rostamy, D.; Baleanu, Dumitru; Alipour, M.; Jafari, H.; Baleanu, D.; MatematikIn this paper, we present a numerical method for solving a class of fractional differential equations (FDEs). Based on Bernstein Polynomials (BPs) basis, new matrices are utilized to reduce the multi-term orders fractional differential equation to a system of algebraic equations. Convergence analysis is shown by several theorems. Illustrative examples are included to demonstrate the validity and applicability of this method.Article Recent Advances in Special Functions, Fractional Operators and Their Real World Applications(Cambridge Scientific Publishers, 2021) Singh, J.; Baleanu, Dumitru; Baleanu, D.; Kumar, D.; Hammouch, Z.; MatematikThis special issue ”Recent Advances in Special Functions, Fractional Operators and their Real World Applications” of the journal Mathematics in Engineering, Science and Aerospace (MESA) is mainly collection of the research articles presented in 3rd International Conference on Mathematical Mod-elling, Applied Analysis and Computation (ICMMAAC-20) organized by the Department of Mathe-matics, JECRC University, Jaipur, India during August 7-9, 2020. This collection of articles is mainly concerned to address a wide range of special functions, operators of fractional order and their uses in mathematical modelling and computation of distinct problems of physical sciences, chemical sci-ences, biological sciences, engineering sciences, social science and economics. In the this special is-sue, expository and original research papers associated with the new trends and challenges in special functions and fractional order calculus and as well as their uses in real world problems are collected. Some are invited papers. © CSP - Cambridge, UK; I&S - Florida, USA, 2021Article Citation - Scopus: 3On Some Impulsive Fractional Neutral Differential Systems With Nonlocal Condition Through Fractional Operators(Cambridge Scientific Publishers, 2017) Anuradha, A.; Baleanu, Dumitru; Baleanu, D.; Suganya, S.; Arjunan, M.M.; MatematikAccording to semigroup theories, fractional calculus, Banach contraction principle and Schaefer's fixed point theorem, this paper is fundamentally involved with the existence of mild solutions for an impulsive fractional neutral differential systems (abbreviated, IFNDS) with nonlocal conditions (abbreviated, NLC) in Banach space X. At last, an illustration is also presented to exhibit the use of our theoretical results. © CSP - Cambridge, UK; I & S - Florida, USA, 2017.