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DOI：http://dx.doi.org/10.26855/jamc.2022.06.009

# Galerkin Weighted Residual Method for Solving Fourth Order Fractional Differential and Integral Boundary Value Problems

Date: June 20,2022 |Hits: 173 Download PDF How to cite this paper

Umme Ruman1, Md. Shafiqul Islam2,*

1Department of Computer Science & Engineering, Faculty of Science & Engineering, Green University of Bangladesh, Dhaka-1207, Bangladesh.

2Department of Applied Mathematics, University of Dhaka, Dhaka-1000, Bangladesh.

*Corresponding author: Md. Shafiqul Islam

### Abstract

In this research work, the Galerkin weighted residual method is used to find the numerical solution of fourth-order fractional value problems with homogeneous and non-homogeneous boundary conditions. The same approach is applied also to compute the approximate solutions for the two-point fourth-order integro-differential problem in fractional order. The matrix formulation of both cases is enunciated explicitly using piecewise polynomials. The operator expressing the Caputo fractional derivatives is used in this procedure. We experiment various cases from the literature in order to calculate the accuracy and efficacy of the current technique using Legendre and Bernoulli polynomials as bases. We find that the present solutions converge to the exact solutions. The absolute errors are tabulated, and we believe that absolute reliability has been achieved. The proposed method may be implemented to partial differential equations of fractional order.

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### How to cite this paper

Galerkin Weighted Residual Method for Solving Fourth Order Fractional Differential and Integral Boundary Value Problems

How to cite this paper:  Umme Ruman, Md. Shafiqul Islam. (2022) Galerkin Weighted Residual Method for Solving Fourth Order Fractional Differential and Integral Boundary Value Problems. Journal of Applied Mathematics and Computation6(2), 246-255.

DOI: http://dx.doi.org/10.26855/jamc.2022.06.009