Volume 1: Issue 2

Volume 1: Issue 2

On Some Algebraic and Order-Theoretic Aspects of Machine Interval Arithmetic

** Author(s): ** Hend Dawood

** DOI: ** 10.5281/zenodo.2656089

** Keywords : ** Interval mathematics; Machine interval arithmetic; Outward rounding; Floating-point arithmetic; Machine monotonicity; Dense orders; Orderability of intervals; Symmetricity; Singletonicity; Subdistributive semiring; S-semiring

** Refer this article: ** Hend Dawood (2019). On Some Algebraic and Order-Theoretic Aspects of Machine Interval Arithmetic. Online Mathematics Journal, 01(02), 1–13. DOI: 10.5281/zenodo.2656089.

Interval arithmetic is a fundamental and reliable mathematical machinery for scientific computing and for addressing uncertainty in general. In order to apply interval mathematics to real life uncertainty problems, one needs a computerized (machine) version thereof, and so, this article is devoted to some mathematical notions concerning the algebraic system of machine interval arithmetic. After formalizing some purely mathematical ingredients of particular importance for the purpose at hand, we give formal characterizations of the algebras of real intervals and machine intervals along with describing the need for interval computations to cope with uncertainty problems. Thereupon, we prove some algebraic and order-theoretic results concerning the structure of machine intervals.

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A New Fractional Model for the Cancer Treatment by Radiotherapy Using the Hadamard Fractional Derivative

** Author(s): ** M. Awadalla, Y. Y. Yameni, K. Abuassba

** DOI: ** 10.5281/zenodo.3046037

** Keywords : ** Hadamard fractional derivative, Existence and uniqueness, Fixed point theory, Nonlinear fractional differential equation

** Refer this article: ** M. Awadalla, Y .Y. Yameni, & K. Abuassba (2019). A New Fractional Model for the Cancer Treatment by Radiotherapy Using the Hadamard Fractional Derivative. Online Mathematics Journal, 01(02), 14–18. DOI: 10.5281/zenodo.3046037.

In this article, a mathematical model for cancer treatment by radiotherapy is examined. The model is integrated into the Hadamard fractional derivative. First, we examine the existence of the solution. Then, the uniqueness of the solution is investigated.

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Note on Double Aboodh Transform of Fractional Order and its Properties

** Author(s): ** S. Alfaqeih, T. ÖZIS

** DOI: ** 10.5281/zenodo.3047015

** Keywords : ** Fractional Laplace transform , Summudu transform , Double Aboodh transform , Mittag leffler function

** Refer this article: ** S. Alfaqeih, & T. Ozis (2019). Note on Double Aboodh Transform of Fractional Order and its Properties. Online Mathematics Journal, 01(02), 19–25. DOI: 10.5281/zenodo.3047015.

In this study, we introduce definitions of a fractional double Aboodh transform of order α, where α ϵ [0, 1], for a functions which are fractional differentiable. We then establish some main properties of this transform. Furthermore, we prove some related theorems.