Pure and Applied Mathematics Journal

Volume 2, Issue 1, February 2013

  • Definitions of Real Order Integrals and Derivatives Using Operator Approach

    Raoelina Andriambololona

    Issue: Volume 2, Issue 1, February 2013
    Pages: 1-9
    Published: 20 February 2013
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    Abstract: The set E of functions f fulfilling some conditions is taken to be the definition domain of s-order integral operator J^s (iterative integral), first for any positive integer s and after for any positive s (fractional, transcendental π and e). The definition of k-order derivative operator D^k for any positive k (fractional, transcendental π and e) ... Show More
  • Two Definitions of Fractional Derivative of Powers Functions

    Raoelina Andriambololona, Rakotoson Hanitriarivo, Tokiniaina Ranaivoson, Roland Raboanary

    Issue: Volume 2, Issue 1, February 2013
    Pages: 10-19
    Published: 20 February 2013
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    Abstract: We consider the set of powers functions defined on R_+ and their linear combinations. After recalling some properties of the gamma function, we give two general definitions of derivatives of positive and negative integers, positive and negative fractional orders. Properties of linearity and commutativity are studied and the notions of semi-equality... Show More
  • Existence Results for A Nonlocal Problem Involving the p(x)-Laplacian

    Mustafa Avci

    Issue: Volume 2, Issue 1, February 2013
    Pages: 20-27
    Published: 20 February 2013
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    Abstract: In the present paper, we deal with two different existence results of solutions for a nonlocal elliptic Dirichlet boundary value problem involving p(x)-Laplacian. The first one is based on the Brouwer fixed point theorem and the Galerkin method which gives a priori estimate of a nontrivial weak soltion. The second one is based on the variational me... Show More
  • Non Oscillatory Nonlinear Differential Systems with Slowly Varying Coefficients in Presence on Certain Damping Forces

    Pinakee Dey

    Issue: Volume 2, Issue 1, February 2013
    Pages: 28-31
    Published: 20 February 2013
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    Abstract: Krylov-Bogoliubov-Mitropolskii method is modified and applied to certain damped nonlinear systems with slowly varying coefficients. The results obtained by this method show excellent coincidence with those obtained by numerical method. The method is illustrated by an example.
  • About Solutions of Nonlinear Algebraic System with Two Variables

    Rakhshanda Dzhabarzadeh

    Issue: Volume 2, Issue 1, February 2013
    Pages: 32-37
    Published: 20 February 2013
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    Abstract: For nonlinear algebraic system with two variables sufficient conditions of existence of solutions are given. The proof of these statements is received as a corollary of more common reviewing considered in this paper. In particular, in this work the existence of multiple base on eigen and associated vectors of a two parameter system of operators in ... Show More
  • Rhotrix Polynomials and Polynomial Rhotrices

    S. M. Tudunkaya

    Issue: Volume 2, Issue 1, February 2013
    Pages: 38-41
    Published: 20 February 2013
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    Abstract: In this piece of note, polynomials defined over the ring R of rhotrices of n-dimension and rhotrices defined over polynomials in were explored, the aim is to study their nature and present their properties. The hope is that these polynomials (or these rhotrices) will have wider applications than those polynomials defined over the non-commutative ... Show More
  • Modeling the Epidemiology of Malaria and Control with Estimate of the Basic Repro-duction Number

    Adamu Abdul Kareem, Anande Richard Kimbir

    Issue: Volume 2, Issue 1, February 2013
    Pages: 42-50
    Published: 20 February 2013
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    Abstract: Strategies for controlling the epidemiology of many infectious diseases such as malaria include a rapid reduc-tion in both the infected and susceptible population via treatment and vaccination. In this paper, we have modified the Tumwiine et al. (2007) mathematical model for the transmission of malaria by including a vaccination parameter. We have ... Show More