文章基本信息

标题：Higher-dimensional physical models with multimemory indices: analytic solution and convergence analysis
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作者：Imad Jaradat ; Marwan Alquran ; Ruwa Abdel-Muhsen 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2020
卷号：2020
期号：1
页码：1-14
DOI：10.1186/s13662-020-02822-7
出版社：Hindawi Publishing Corporation
摘要：The purpose of this work is to analytically simulate the mutual impact for the existence of both temporal and spatial Caputo fractional derivative parameters in higher-dimensional physical models. For this purpose, we employ the γ̅-Maclaurin series along with an amendment of the power series technique. To supplement our idea, we present the necessary convergence analysis regarding the γ̅-Maclaurin series. As for the application side, we solved versions of the higher-dimensional heat and wave models with spatial and temporal Caputo fractional derivatives in terms of a rapidly convergent γ̅-Maclaurin series. The method performed extremely well, and the projections of the obtained solutions into the integer space are compatible with solutions available in the literature. Finally, the graphical analysis showed a possibility that the Caputo fractional derivatives reflect some memory characteristics.
关键词：Memory index;Fractional PDEs;Analytic solution;