Abstract
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.
Highlights
The differential transform scheme is a method for solving a wide range of problems whose mathematical models yield equations or systems of equations classified as algebraic, differential, integral and integro-differential.[1,2,3] The concept of differential transform was first proposed by Zhou,[4] and its main applications therein are solved for both linear and non-linear initial value problems in electric circuit analysis
This method constructs an analytical solution in the form of polynomials
The differential transform method (DTM) is an iterative procedure that is used to obtain analytic Taylor series solutions of differential equations. This method results in the construction of an analytical solution in the form of polynomials
Summary
The differential transform scheme is a method for solving a wide range of problems whose mathematical models yield equations or systems of equations classified as algebraic, differential, integral and integro-differential.[1,2,3] The concept of differential transform was first proposed by Zhou,[4] and its main applications therein are solved for both linear and non-linear initial value problems in electric circuit analysis. The differential transform method (DTM) is an iterative procedure that is used to obtain analytic Taylor series solutions of differential equations. Nazari and Shahmorad[8] used the DTM to solve the fractional-order integro-differential equations with non-local boundary conditions. The reduced differential transform method (RDTM) has been introduced by Keskin and Oturanc for solving partial differential equations (PDEs).
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