Document Type
Article
Publication Date
11-2021
Abstract
A multidimensional, modified, fractional-order B-polys technique was implemented for finding solutions of linear fractional-order partial differential equations. To calculate the results of the linear Fractional Partial Differential Equations (FPDE), the sum of the product of fractional B-polys and the coefficients was employed. Moreover, minimization of error in the coefficients was found by employing the Galerkin method. Before the Galerkin method was applied, the linear FPDE was transformed into an operational matrix equation that was inverted to provide the values of the unknown coefficients in the approximate solution. A valid multidimensional solution was determined when an appropriate number of basis sets and fractional-order of B-polys were chosen. In addition, initial conditions were applied to the operational matrix to seek proper solutions in multidimensions. The technique was applied to four examples of linear FPDEs and the agreements between exact and approximate solutions were found to be excellent. The current technique can be expanded to find multidimensional fractional partial differential equations in other areas, such as physics and engineering fields.
Recommended Citation
Bhatti, M.I.; Rahman, M.H. Technique to Solve Linear Fractional Differential Equations Using B-Polynomials Bases. Fractal Fract. 2021, 5, 208. https://doi.org/10.3390/fractalfract5040208
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Publication Title
Fractal and Fractional
DOI
10.3390/fractalfract5040208
Comments
© 2021 by the authors.