A generalized analytical approach for highly accurate solutions of fractional differential equations

A generalized homotopy-based approach is developed to give highly accurate solutions of fractional differential equations. By introducing a scaling transformation, the computational domain of the nonlinear Riccati differ-ential equations with fractional order changes from [0,+infinity) to [0,1]. Analytical approximation of arbitrary ac-curacy is achieved, whose convergence is proved theoretically. The effectiveness and accuracy of our solution is strictly checked via error analysis. The proposed method is expected to be as a new and reliable analytical approach to give highly accurate solutions of strongly nonlinear problems in fractional calculus.

Automated summary

A generalized homotopy-based approach is developed to provide highly accurate solutions for fractional differential equations. By introducing a scaling transformation, the computational domain of the nonlinear Riccati differential equations is reduced to [0,1]. The proposed method is shown to be effective and accurate through error analysis, making it a reliable analytical approach for solving strongly nonlinear problems in fractional calculus.