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Mathematics, Volume 7, Issue 2

February 2019 - 103 articles

Cover Story: Derivatives and integrals of arbitrary non-integer (fractional) order were introduced by Leibniz, Euler, Liouville, Riemann,Weyl, and other prominent mathematicians. In this article, we propose desiderata for calling an operator a fractional derivative or a fractional integral based on a small number of time honoured and well established criteria. View this paper.
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Articles (103)

  • Article
  • Open Access
14 Citations
3,762 Views
16 Pages

25 February 2019

In this research, a singly diagonally implicit block backward differentiation formulas (SDIBBDF) for solving stiff ordinary differential equations (ODEs) is proposed. The formula reduced a fully implicit method to lower triangular matrix with equal d...

  • Article
  • Open Access
20 Citations
3,755 Views
20 Pages

24 February 2019

When analyzing the possibility of supporting the decision-making process, one should take into account the essential properties of economic entities (the system and its objects). As a result, the development of an effective business model ought to be...

  • Article
  • Open Access
5 Citations
3,840 Views
9 Pages

More Results on the Domination Number of Cartesian Product of Two Directed Cycles

  • Ansheng Ye,
  • Fang Miao,
  • Zehui Shao,
  • Jia-Bao Liu,
  • Janez Žerovnik and
  • Polona Repolusk

24 February 2019

Let γ ( D ) denote the domination number of a digraph D and let C m □ C n denote the Cartesian product of C m and C n , the directed cycles of length n ≥ m ≥ 3 . Liu et al. obtained the exact valu...

  • Article
  • Open Access
77 Citations
3,915 Views
17 Pages

Nonlocal Fractional Evolution Inclusions of Order α ∈ (1,2)

  • Jia Wei He,
  • Yong Liang,
  • Bashir Ahmad and
  • Yong Zhou

24 February 2019

This paper studies the existence of mild solutions and the compactness of a set of mild solutions to a nonlocal problem of fractional evolution inclusions of order α ∈ ( 1 , 2 ) . The main tools of our study include the concepts of...

  • Article
  • Open Access
7 Citations
3,220 Views
8 Pages

23 February 2019

Fractional calculus image formulas involving various special functions are important for evaluation of generalized integrals and to obtain the solution of differential and integral equations. In this paper, the Saigo’s fractional integral opera...

  • Article
  • Open Access
8 Citations
3,394 Views
12 Pages

23 February 2019

We present a local convergence of the combined Newton-Kurchatov method for solving Banach space valued equations. The convergence criteria involve derivatives until the second and Lipschitz-type conditions are satisfied, as well as a new center-Lipsc...

  • Article
  • Open Access
4 Citations
2,976 Views
8 Pages

22 February 2019

We consider Ulisse Dini-type helicoidal hypersurfaces with timelike axis in Minkowski 4-space E 1 4 . Calculating the Gaussian and the mean curvatures of the hypersurfaces, we demonstrate some special symmetries for the curvatures when they...

  • Article
  • Open Access
3 Citations
3,343 Views
12 Pages

Stanley Depth of Edge Ideals of Some Wheel-Related Graphs

  • Jia-Bao Liu,
  • Mobeen Munir,
  • Raheel Farooki,
  • Muhammad Imran Qureshi and
  • Quratulien Muneer

21 February 2019

Stanley depth is a geometric invariant of the module and is related to an algebraic invariant called depth of the module. We compute Stanley depth of the quotient of edge ideals associated with some familiar families of wheel-related graphs. In parti...

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Mathematics - ISSN 2227-7390