The method to solve nonlinear partial fractional differential equation using fractional Bhatti-polynomial BasesMd. Habibur Rahman, Muhammad I. Bhatti*, and Nicholas DimakisUniversity of Texas Rio Grande Valley, Edinburg, Texas, 78539*Corresponding author: Muhammad.bhatti@utrgv.edu

The multidimensional modified fractional-order B-polys technique has been used to discover solutions to nonlinear partial fractional differential equations. It incorporates a multivariable approach for estimating solutions of nonlinear fractional-order partial differential equations. The sum of the product of the fractional B-polys and the expansion coefficients is used to compute the solutions of the nonlinear fractional partial differential equations (NFPDE). The Galerkin technique is also used to minimize the error in the coefficients of the expansion. The estimated solution is produced by converting the NFPDE into an operational matrix equation and then inverted to determine the values of the unknown coefficients. Using the initial guess from the linear component of the NFPDE, the nonlinear parts of the NFPDE are merged in the operational matrix equation and iterated until converged values for coefficients are found. When a suitable degree of B-poly basis is used, and the initial conditions are imposed on the operational matrix before invoking inverse, a valid converged solution of NFPDE is obtained. The present method may be extended to solve multidimensional linear and nonlinear fractional partial differential equations in other scientific disciplines, such as physics and engineering. In the present study, the approximative solutions to four NFDEs have been computed using this approach, proving the method’s validity. The approximate answers to the differential equations have also been compared with known precise and numerical answers-- an excellent agreement is found between them.