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Published in:   Vol. 3 Issue 3 Date of Publication:   December 2014

Fractal Boundary Value Problems for Integral and Differential Equations with Local Fractional Operators

T. Henson,R. Malarkodi

Page(s):   226-228 ISSN:   2278-2397
DOI:   10.20894/IJCOA. Publisher:   Integrated Intelligent Research (IIR)

In this paper, the local fractional decomposition method is applied to investigate the fractal boundary value problems for the Volterra integral equations and heat conduction equations. The accuracy and reliability of the obtained results of explained using examples.Fractal is a mathematical set that typically displays self-similar patterns. Fractals are usually nowhere differentiable. These fractals are used in many engineering applications such as porous media modelling, nano fluids, fracture mechanics and many other applications in nanoscale. The fractals nature of the objects must be taken into account in various transport phenomena. The local temperature depends on the fractal dimensions for the transport phenomena in the fractals object. To solve the linear and non-linear problems of ordinary, partial differential equation and integral equations, Adomain introduced a method called the decomposition method. Also inorder to investigate local fractal behaviours of differential equations with fractal conditions,a new tool has been designed called the local fractional derivation.The local fractional variational iteration method local fractional decomposition method etc, are the analytical methods used to solve the differential and integral equations with fractional derivative and integral operator.