Approximate series solution of multi-dimensional, time fractional-order (heat-like) diffusion equations using FRDTM

被引：32
作者：
Singh, Brajesh K. [1 ]
Srivastava, Vineet K. [2 ]
机构：
[1] Babasaheb Bhimrao Ambedkar Univ, Dept Appl Math, Lucknow 226025, Uttar Pradesh, India
[2] ISRO Telemetry Tracking & Command Network ISTRAC, Bangalore 560058, Karnataka, India
来源：
ROYAL SOCIETY OPEN SCIENCE | 2015年 / 2卷 / 04期
关键词：
multi-dimensional diffusion equation; Caputo time-fractional derivative; Mittag-Leffler function; fractional-order reduced differential transform method; exact solution; VARIATIONAL ITERATION METHOD; HOMOTOPY PERTURBATION METHOD; PARTIAL-DIFFERENTIAL-EQUATIONS; COMPACT; SCHEME;
D O I：
10.1098/rsos.140511
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multidimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations.
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页数：13
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