A Short Note on the Quasilinearization Method for Fractional Differential Equations

ABSTRACT

Recent literature shows that for certain classes of fractional differential equations the monotone iterative technique fails to guarantee the quadratic convergence of the quasilinearization method. The present work proves the quadratic convergence of the quasilinearization method and the existence and uniqueness of the solution of such a class of fractional differential equations. Our analysis depends upon the classical Kantorovich theorem on Newton's method. Various examples are discussed in order to illustrate our approach.

KEYWORDS:

• Caputo's fractional derivative
• fractional order Riccati equation
• Newton's method
• quasilinearization

MATHEMATICS SUBJECT CLASSIFICATION:

• 34A08
• 34A12
• 65J15

Acknowledgement

The author wishes to express his utmost gratitude to Prof. P. V. Subrahmanyam, IIT Madras, for his valuable suggestion and his initial guidance. The author extend his thanks to Dr. G. Chandhini, Assistant Professor, NIT Karnataka Surathkal, India for her help regarding the MATLAB code.