Reduced differential transform method for partial differential equations within local fractional derivative operators

The non-differentiable solution of the linear and non-linear partial differential equations on Cantor sets is implemented in this article. The reduced differential transform method is considered in the local fractional operator sense. The four illustrative examples are given to show the efficiency and accuracy features of the presented technique to solve local fractional partial differential equations.

[1]  H. Srivastava,et al.  Local Fractional Integral Transforms and Their Applications , 2015 .

[2]  Hossein Jafari,et al.  On the Exact Solution of Wave Equations on Cantor Sets , 2015, Entropy.

[3]  Sunil Kumar,et al.  A new analytical modelling for fractional telegraph equation via Laplace transform , 2014 .

[4]  I. Ozkol,et al.  Solution of fractional integro-differential equations by using fractional differential transform method , 2009 .

[5]  Fatma Ayaz,et al.  Applications of differential transform method to differential-algebraic equations , 2004, Appl. Math. Comput..

[6]  Yildiray Keskin,et al.  Reduced Differential Transform Method for Partial Differential Equations , 2009 .

[7]  J. Biazar,et al.  Differential Transform Method for Systems of Volterra Integral Equations of the First Kind , 2010 .

[8]  Yang Xiaojun,et al.  Local Fractional Calculus and Its Applications , 2012 .

[9]  S. Shahmorad,et al.  Application of the fractional differential transform method to fractional-order integro-differential equations with nonlocal boundary conditions , 2010, J. Comput. Appl. Math..

[10]  Ji-Huan He,et al.  Geometrical explanation of the fractional complex transform and derivative chain rule for fractional calculus , 2012 .

[11]  Hossein Jafari,et al.  Local Fractional Adomian Decomposition and Function Decomposition Methods for Laplace Equation within Local Fractional Operators , 2014 .

[12]  Ahmed Elsaid.  Fractional differential transform method combined with the Adomian polynomials , 2012, Appl. Math. Comput..

[13]  Ibrahim Özkol,et al.  Solution of difference equations by using differential transform method , 2006, Appl. Math. Comput..

[14]  Ji-Huan He.  A NEW FRACTAL DERIVATION , 2011 .

[15]  Hari M. Srivastava,et al.  A new numerical technique for solving the local fractional diffusion equation: Two-dimensional extended differential transform approach , 2016, Appl. Math. Comput..