Exact and Approximate Solution of Multi-Higher Order Fractional Differential Equations Via Sawi Transform and Sequential Approximation Method

Abstract

Background

        In this paper, we propose two new techniques called the Sawi transformations and Sequential approximations method, which are applied to solve multi-higher order linear fractional differential equations with constant coefficients. In which Riemann-Liouville and Caputo define the fractional derivatives and fractional integral, fractional formula for all types have been derived, we first developed the Sawi transform of foundational mathematical functions for this purpose and then described the important characteristics of the Sawi transform, which may be applied to solve ordinary differential equations and fractional differential equations. Following that, the authors found an exact solution to a particular example of fractional differential equations.

Materials and Methods

       With these methods good exact and approximate solutions can be obtained with only a few iterations for the Sequential approximations method, and the approximate solutions guarantee the desired accuracy. For more validation of the methods, and fractional formula of sawi transformation method work such as other transformation.

Results:    The exact and approximation solutions for some fractional differential equations are obtained, and several examples are explained to demonstrate the efficiency and implementation of the proposed methods.

Conclusions

      It is clear from reading the literature on fractional differential equations (FDEs) that the Sawi transformation method is a workable solution to these problems. To use this approach, which also completely resolved fractional differential equations, the FDEs must be simplified.