On Caputo–Hadamard fractional differential equations

ABSTRACT

In this paper, the existence and uniqueness of solution to Caputo–Hadamard fractional differential equation (FDE) are studied. The continuation theorem is established too. Then, Euler and predictor–corrector methods are built up to solve Caputo–Hadamard FDE. The stability and error analysis of the derived numerical schemes are investigated as well. At last, a numerical example is carried out to verify the numerical algorithm.

KEYWORDS:

• Caputo–Hadamard derivative
• fractional differential equation
• existence and uniqueness
• continuation theorem
• Euler method
• predictor–corrector method

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 26A33
• 34A08

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The present job was partially supported by the National Natural Science Foundation of China [grant number 11872234].