Publications

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    Angelina M. Bijura
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    ABSTRACT: The solution of a singularly perturbed type of a system of fractional integral (differential) equations is studied in this paper. The formal asymptotic solution is derived and proved to be asymptotically correct. Basic matrix algebra is used to prove the asymptotic decay in the inner layer solution.
    Journal of Integral Equations and Applications 01/2012; 24(2012). · 0.61 Impact Factor
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    Angelina M. Bijura
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    ABSTRACT: It is demonstrated here that there exist initial layers to singularly perturbed Volterra equations whose thicknesses are not of the order of magnitude of O(ϵ), ϵ → 0. It is also shown that the initial-layer theory is extremely useful because it allows one to construct the approximate solution to an equation, which is almost identical to the exact solution.
    IMA Journal of Applied Mathematics 01/2006; · 1.17 Impact Factor
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    Angelina M. Bijura
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    ABSTRACT: Asymptotic solutions of nonlinear singularly perturbed Volterra integral equations with kernels possessing integrable singularity are investigated using singular perturbation methods and the Mellin transform technique. In particular, it is demonstrated that the formal approximation is asymptotically valid.
    Journal of Applied Mathematics 12/2004; · 0.83 Impact Factor
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    Angelina M. Bijura
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    ABSTRACT: Nonlinear singularly perturbed Volterra integrodifferential equations with weakly singular kernels are investigated using singular perturbation methods, the Mellin transform technique, and the theory of fractional integration.
    International Journal of Mathematics and Mathematical Sciences 01/2003;
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    Angelina M. Bijura
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    ABSTRACT: The additive decomposition singular perturbation method and the theory of fractional integration are used to study asymptotic solutions of singularly perturbed Volterra integrodifferential equations with kernels having integrable singularity. The validity of the approximation is also demonstrated.
    International Journal of Mathematics and Mathematical Sciences 01/2003;
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    Angelina Bijura
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    ABSTRACT: We consider finding asymptotic solutions of the singularly perturbed linear Volterra in- tegral equations with weakly singular kernels. An interesting aspect of these problems is that the discontinuity of the kernel causes layer solutions to decay algebraically rather than exponentially within the initial (boundary) layer. To analyse this phenomenon, the paper demonstrates the similarity that these solutions have to a special function called the Mittag-Leffler function.
    International Journal of Mathematics and Mathematical Sciences 01/2002;
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    A. M. Bijura
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    ABSTRACT: This paper studies the behaviour of the solution u(t,ε) of the system of Volterra integral equations εu(t)=f(t)+∫ 0 t A(t,s)u(s)ds,0≤t≤T, as the positive parameter ϵ tends to zero. Both f and A are continuous, and the eigenvalues of A(t,t) are supposed to be negative. For small values of ε this leads to a fast exponential decay within a small boundary layer. The additive decomposition technique (originally developed by O’Malley and Hoppensteadt) is used to obtain an asymptotic power series expansion of u(t,ϵ) in the parameter ϵ. From this series an approximant is constructed with the property that the difference of the true solution and this approximant tends to zero uniformly on the interval [0,T] as ϵ→0. The theory is illustrated by means of two examples. In the latter of these examples the decay is not exponential within the boundary layer.
    Journal of Applied Analysis. 01/2002; 8(2):221-244.

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