Bell collocation method for solving fractional order differential equations and systems

The present thesis investigates the approximate solutions of fractional order linear differential equations and systems of equations. The existence of analytical solutions to these equations is either non-existent or difficult to obtain. The collocation method, an effective numerical solution technique, is presented in this study, which is based on generalized Bell functions. In the proposed methodology, the approximate solution function is expressed in terms of the truncated Bell series. The matrix relations of the default solution and conditions are formed. The system of fractional equations is reduced to a system of algebraic equations by including collocation points in the matrix relations, with these points equally spaced. The coefficients of the Bell series are obtained by solving this reduced system. In this study, a range of examples with differing structural characteristics are presented to demonstrate the applicability of the method. The results obtained are then compared with the existing exact solutions and the solutions of other existing methods in the literature. This comparison is made to demonstrate the effectiveness of the method. It is observed that the results obtained are in agreement with the exact solutions, or the margin of error is negligible. The software program MATLAB was utilized for the purpose of calculation and the generation of graphical representations for comparison. The method's compatibility with computer-aided applications facilitates the resolution of diverse fraction degrees and complex equation systems, thereby reducing the overall working time.