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Fractional Order Airy’s Type Differential Equations of Its Models Using RDTM
- Source :
- Mathematical Problems in Engineering, Vol 2021 (2021)
- Publication Year :
- 2021
- Publisher :
- Hindawi Limited, 2021.
-
Abstract
- In this paper, we propose a novel reduced differential transform method (RDTM) to compute analytical and semianalytical approximate solutions of fractional order Airy’s ordinary differential equations and fractional order Airy’s and Airy’s type partial differential equations subjected to certain initial conditions. The performance of the proposed method was analyzed and compared with a convergent series solution form with easily computable coefficients. The behavior of approximated series solutions at different values of fractional order α and its modeling in 2-dimensional and 3-dimensional spaces are compared with exact solutions using MATLAB graphical method analysis. Moreover, the physical and geometrical interpretations of the computed graphs are given in detail within 2- and 3-dimensional spaces. Accordingly, the obtained approximate solutions of fractional order Airy’s ordinary differential equations and fractional order Airy’s and Airy’s type partial differential equations subjected to certain initial conditions exactly fit with exact solutions. Hence, the proposed method reveals reliability, effectiveness, efficiency, and strengthening of computed mathematical results in order to easily solve fractional order Airy’s type differential equations.
- Subjects :
- Partial differential equation
Article Subject
Series (mathematics)
Differential equation
General Mathematics
General Engineering
Type (model theory)
Engineering (General). Civil engineering (General)
Ordinary differential equation
QA1-939
Order (group theory)
Applied mathematics
TA1-2040
MATLAB
computer
Mathematics
Convergent series
computer.programming_language
Subjects
Details
- ISSN :
- 15635147 and 1024123X
- Volume :
- 2021
- Database :
- OpenAIRE
- Journal :
- Mathematical Problems in Engineering
- Accession number :
- edsair.doi.dedup.....e2bf8d36abc1479f87a78ba96df70501