Local Fractional Variational Yang-Laplace Method for solving local fractional partial differential Equations
Subject Areas : Statistics
homa afraz
1
,
Jafar Saberi nadjafi
2
1 - PhD Student, Department of Applied Mathematics (Numerical Analysis), Faculty of Mathematics, Ferdowsi University, Mashhad, Iran
2 - Professor, Department of Applied Mathematics (Numerical Analysis), Faculty of Mathematics, Ferdowsi University, Mashhad, Iran
Keywords: تبدیل یانگ -لاپلاس, مشتق کسری موضعی, روش تکرارتغییراتی کسری موضعی, مجموعه کانتور, حساب کسری موضعی,
Abstract :
In the last decade, the theory of local fractional calculus has been successfully used to describe and solve fundamental science and engineering problems. In this article, the local fractional Yang-Laplace variational iteration method has been used for solving the local fractional partial differential equation on a cantor set. The non-differentiable exact and approximate solutions are obtained for kind of local fractional linear and nonlinear equations. It is shown that the used method is an efficient and easy method to implement for linear and nonlinear problems arising in science and engineering. In this article, we emphasize on the LFYLVM method which is a combination form of local fractional variational iteration method and Yang-Laplace transform. Most of the obtained solutions from this method are in series form that converge rapidly to exact or approximate solutions. Illustrative examples demonstrate that the method is able to reduce the volume of computation compared to the existing classical methods.
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