A New Numerical Approach for the Analysis of Variable Fractal and Fractional Order Differential Equations

被引：2

作者：

Jena P. ^{[1
]}

Mohapatra S.N. ^{[1
]}

Mishra S.R. ^{[1
]}

机构：

[1] Department of Mathematics, Siksha ‘O’Anusandhan Deemed to Be University, Odisha, Bhubaneswar

来源：

International Journal of Applied and Computational Mathematics | 2022年 / 8卷 / 4期

关键词：

Error analysis; Fractal-fractional differential equations; Lagrange interpolation;

D O I：

10.1007/s40819-022-01384-4

中图分类号：

学科分类号：

摘要：

The variable fractional dimensions differential and integral operator overrides the phenomenon of the constant fractional order. This leads to exploring some new ideas in the proposed direction due to its varied applications in the recent era of science and engineering. The present papers deal with the replacement of the constant fractional order by variable fractional order in various fractal-fractional differential equations. An advanced numerical scheme is developed with the help of Lagrange three-point interpolation and further, it is employed for the solution of the proposed differential equations. However, the properties of these new operators are presented in detail. Finally, the error analysis is also conducted for the numerical scheme deployed. The results are validated by the suitable choice of applications to real-life problems. The well- known multi-step-Adams–Bashforth numerical scheme for classical differential equations is recovered when the non-integer order is one. © 2022, The Author(s), under exclusive licence to Springer Nature India Private Limited.

引用

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