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.
Highlights
In real-world scientific phenomena, most problems follow either linearity or nonlinearity in their systems
The current study focuses on linear fractional-order differential equations using the generalized Galerkin method [36] and the Bhatti polynomial (B-poly) basis of fractional-order
In set technique to determine the solutions to the partial fractional differential equations
Summary
In real-world scientific phenomena, most problems follow either linearity or nonlinearity in their systems. In several papers [31,32,33,34,35,36], using the B-poly basis of fractional-order and a generalized Galerkin method, the authors were able to find solutions to the fractional-order partial differential equations. The current study seeks solutions to four examples of linear fractional-order partial differential equations using the fractional-order B-poly technique. We present analytical formulism to employ Caputo’s fractional-order derivative on the polynomials, present the process used to create fractional-order basis sets, and develop an algorithm to resolve various linear fractional-order partial differential equations. We apply this technique to four examples. We shall present an error analysis of one of the fourth considered examples
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
