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Applications of Homogenous Balance Principles Combined with Fractional Calculus Approach and Separate Variable Method on Investigating Exact Solutions to Multidimensional Fractional Nonlinear PDEs
Joint Authors
Rui, Weiguo
Ren, Ruichao
Zhang, Shunli
Source
Mathematical Problems in Engineering
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-21, 21 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-05-06
Country of Publication
Egypt
No. of Pages
21
Main Subjects
Abstract EN
We investigate the exact solutions of multidimensional time-fractional nonlinear PDEs (fnPDEs) in this paper.
In terms of the fractional calculus properties and the separate variable method, we present a new homogenous balance principle (HBP) on the basis of the (1 + 1)-dimensional time fnPDEs.
Taking advantage of the new types of HBP together with fractional calculus formulas that subtly avoid the chain rule, the fnPDEs can be reduced to spatial PDEs, and then we solve these PDEs by the fractional calculus method and the separate variable approach.
In this way, some new type exact solutions of the certain time-fractional (2 + 1)-dimensional KP equation, (3 + 1)-dimensional Zakharov–Kuznetsov (ZK) equation, and Jimbo–Miwa (JM) equation are explicitly obtained under both Riemann–Liouville derivatives and Caputo derivatives.
The dynamical analysis of solutions is shown by numerical simulations of taking property parameters as well.
American Psychological Association (APA)
Ren, Ruichao& Zhang, Shunli& Rui, Weiguo. 2020. Applications of Homogenous Balance Principles Combined with Fractional Calculus Approach and Separate Variable Method on Investigating Exact Solutions to Multidimensional Fractional Nonlinear PDEs. Mathematical Problems in Engineering،Vol. 2020, no. 2020, pp.1-21.
https://search.emarefa.net/detail/BIM-1201999
Modern Language Association (MLA)
Ren, Ruichao…[et al.]. Applications of Homogenous Balance Principles Combined with Fractional Calculus Approach and Separate Variable Method on Investigating Exact Solutions to Multidimensional Fractional Nonlinear PDEs. Mathematical Problems in Engineering No. 2020 (2020), pp.1-21.
https://search.emarefa.net/detail/BIM-1201999
American Medical Association (AMA)
Ren, Ruichao& Zhang, Shunli& Rui, Weiguo. Applications of Homogenous Balance Principles Combined with Fractional Calculus Approach and Separate Variable Method on Investigating Exact Solutions to Multidimensional Fractional Nonlinear PDEs. Mathematical Problems in Engineering. 2020. Vol. 2020, no. 2020, pp.1-21.
https://search.emarefa.net/detail/BIM-1201999
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1201999