A modified quasilinearization method for fractional differential equations and its applications

• A modification on quasilinearization method for FDE has been proposed.
• The proposed method relaxes the monotone condition on the derivative of F(t, x).
• The method is illustrated using examples and compared with recent numerical methods.
• More robust with less computational complexity compared to existing quasilinearization.
• Performs even better than the generalised quasilinearization in some cases.

In this paper, we prove an existence and uniqueness theorem for solving the nonlinear fractional differential equation of Caputo’s type of order q ∈ (0, 1] using the method of modified quasilinearization. The main theorem has been illustrated numerically using appropriate examples which shows that the proposed quasilinearization method is robust and easy to apply.