We propose a new definition of a fractional-order Sumudu transform for fractional differentiable functions. In the development of the definition we use fractional analysis based on the modified Riemann-Liouville derivative that we name the fractional Sumudu transform. We also established a relationship between fractional Laplace and Sumudu duality with complex inversion formula for fractional Sumudu transform and apply new definition to solve fractional differential equations.

V. G. Gupta

Bhavna Shrama

Adem Kiliçman

A Note on Fractional Sumudu Transform

We study several criteria for the (non)linearity of Costas permutations, with or without the
imposition of additional algebraic structure in the domain and the range of the permutation, aiming
to find one that successfully identifies Costas permutations as more nonlinear than randomly chosen
permutations of the same order.

Konstantinos Drakakis

On the Measurement of the (Non)linearity of Costas Permutations

The purpose of this paper is to present a uniform finite difference method for numerical solution of nonlinear singularly perturbed convection-diffusion problem with nonlocal and third type boundary conditions. The numerical method is constructed on piecewise uniform Shishkin type mesh. The method is shown to be convergent, uniformly in the diffusion parameter <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>&#x03B5;</mml:mi></mml:math>, of first order in the discrete maximum norm. Some numerical experiments illustrate in practice the result of convergence proved theoretically.

Musa &#199;ak&#305;r

Gabil M. Amiraliyev

A Numerical Method for a Singularly Perturbed Three-Point Boundary Value Problem

We study an inhomogeneous partial differential equation which includes a separate edge detection part to control smoothing in and around possible discontinuities, under the framework of
anisotropic diffusion. By incorporating edges found at multiple scales
via an adaptive edge detector-based indicator function, the proposed
scheme removes noise while respecting salient boundaries. We create
a smooth transition region around probable edges found and reduce
the diffusion rate near it by a gradient-based diffusion coefficient. In
contrast to the previous anisotropic diffusion schemes, we prove the
well-posedness of our scheme in the space of bounded variation. The
proposed scheme is general in the sense that it can be used with any
of the existing diffusion equations. Numerical simulations on noisy
images show the advantages of our scheme when compared to other
related schemes.

V. B. Surya Prasath

Arindama Singh

Well-Posed Inhomogeneous Nonlinear Diffusion Scheme for Digital Image Denoising

This paper provides the analytic solution to the partial differential equation for the value of a convertible bond. The equation assumes a Vasicek model for the interest rate and a geometric Brownian motion model for the stock price. The solution is obtained using integral transforms.

A. S. Deakin

Matt Davison

An Analytic Solution for a Vasicek Interest Rate Convertible Bond Model

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Journal of Applied Mathematics publishes original research papers and review articles in all areas of applied, computational, and industrial mathematics.

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Chief Editor, Professor Theodore E. Simos, is based at Ulyanovsk State Technical University, Russia. His main research interest is the numerical analysis of differential equations.

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Journal of Applied Mathematics - Table of contents 2010

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Journal of Applied Mathematics publishes original research papers and review articles in all areas of applied, computational, and industrial mathematics.

Journal of Applied Mathematics