Matematik Bölümü Yayın Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413

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  • 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.; Matematik
    This 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, 2021
  • Article
    Citation - Scopus: 11
    Oscillation Result for Half-Linear Delay Di Erence Equations of Second-Order
    (American Institute of Mathematical Sciences, 2022) Santra, S.S.; Baleanu, D.; Edwan, R.; Govindan, V.; Murugesan, A.; Altanji, M.; Jayakumar, C.
    In this paper, we obtain the new single-condition criteria for the oscillation of secondorder half-linear delay difference equation. Even in the linear case, the sharp result is new and, to our knowledge, improves all previous results. Furthermore, our method has the advantage of being simple to prove, as it relies just on sequentially improved monotonicities of a positive solution. Examples are provided to illustrate our results. © 2022 the Author(s), licensee AIMS Press.
  • Article
    Citation - WoS: 20
    Citation - Scopus: 36
    On a Singular System of Fractional Nabla Difference Equations With Boundary Conditions
    (Springeropen, 2013) Baleanu, Dumitru I.; Dassios, Ioannis K.
    In this article, we study a boundary value problem of a class of linear singular systems of fractional nabla difference equations whose coefficients are constant matrices. By taking into consideration the cases that the matrices are square with the leading coefficient matrix singular, square with an identically zero matrix pencil and non-square, we provide necessary and sufficient conditions for the existence and uniqueness of solutions. More analytically, we study the conditions under which the boundary value problem has a unique solution, infinite solutions and no solutions. Furthermore, we provide a formula for the case of the unique solution. Finally, numerical examples are given to justify our theory.
  • Article
    Citation - WoS: 30
    Citation - Scopus: 46
    On Non-Homogeneous Singular Systems of Fractional Nabla Difference Equations
    (Elsevier Science inc, 2014) Baleanu, Dumitru I.; Kalogeropoulos, Grigoris I.; Dassios, Ioannis K.
    In this article we study the initial value problem of a class of non-homogeneous singular systems of fractional nabla difference equations whose coefficients are constant matrices. By taking into consideration the cases that the matrices are square with the leading coefficient singular, non-square and square with a matrix pencil which has an identically zero determinant, we provide necessary and sufficient conditions for the existence and uniqueness of solutions. More analytically we study the conditions under which the system has unique, infinite and no solutions. Furthermore, we provide a formula for the case of the unique solution. Finally, numerical examples are given to justify our theory. Crown Copyright (C) 2013 Published by Elsevier Inc. All rights reserved.
  • Article
    Citation - WoS: 23
    Citation - Scopus: 32
    Duality of Singular Linear Systems of Fractional Nabla Difference Equations
    (Elsevier Science inc, 2015) Baleanu, Dumitru I.; Dassios, Ioannis K.
    The main objective of this article is to provide a link between the solutions of an initial value problem of a linear singular system of fractional nabla difference equations, its proper dual system and its transposed dual system. By taking into consideration the case that the coefficients are square constant matrices with the leading coefficient singular, we study the prime system and by using the invariants of its pencil we give necessary and sufficient conditions for existence and uniqueness of solutions. After we prove that by using the pencil of the prime system we can study the existence and uniqueness of solutions of the proper dual system and the transposed dual system. Moreover their solutions, when they exist, can be explicitly represented without resorting to further processes of computations for each one separately. Finally, numerical examples are given based on a singular fractional nabla real dynamical system to justify our theory. (C) 2014 Elsevier Inc. All rights reserved.