Abstract
In this paper, we propose a new type (n + 1)-dimensional reduced differential transform method (RDTM) based on a local fractional derivative (LFD) to solve (n + 1)-dimensional local fractional partial differential equations (PDEs) in Cantor sets. The presented method is named the (n + 1)-dimensional local fractional reduced differential transform method (LFRDTM). First the theories, their proofs and also some basic properties of this procedure are given. To understand the introduced method clearly, we apply it on the (n + 1)-dimensional fractal heat-like equations (HLEs) and wave-like equations (WLEs). The applications show that this new technique is efficient, simply applicable and has powerful effects in (n + 1)-dimensional local fractional problems.
Highlights
The importance of fractional calculus and its popularity have increased during the past four decades, due to its applications in many fields of engineering and applied science
The use of local fractional derivative (LFD) with DTM and RDTM was introduced as local fractional DTM (LFDTM) [27] and local fractional reduced differential transform method (LFRDTM) [28]
We introduce the (n + 1)-dimensional case of RDTM
Summary
The importance of fractional calculus and its popularity have increased during the past four decades, due to its applications in many fields of engineering and applied science. The analysis of entropy in fractional dynamic systems was proposed in [10] Non-differentiable production of entropy in heat conduction of the fractal temperature field was studied in [13]. The method was applied to solve linear, nonlinear, ordinary, partial and fractional order differential equation problems in biology, engineering, physics [41,42,43,44,45,46,47,48,49] and so on. The use of LFD with DTM and RDTM was introduced as local fractional DTM (LFDTM) [27] and local fractional reduced differential transform method (LFRDTM) [28].
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