Temporal discretization for Caputo–Hadamard fractional derivative with incomplete Gamma function via Whittaker function

• Published in: Computational & applied mathematics Vol. 40; no. 8
• Main Authors: Toh, Yoke Teng, Phang, Chang, Ng, Yong Xian
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.12.2021; Springer Nature B.V
• Subjects: Applications of Mathematics; Applied physics; Computational mathematics; Computational Mathematics and Numerical Analysis; Derivatives; Discretization; Gamma function; Mathematical Applications in Computer Science; Mathematical Applications in the Physical Sciences; Mathematics; Mathematics and Statistics; Ordinary differential equations; Partial differential equations; Truncation errors; Caputo–Hadamard fractional derivative; Whittaker M function; Fractional differential equation; 26A33; 35R11; Incomplete Gamma function; Temporal discretization
• ISSN: 2238-3603; 1807-0302
• DOI: 10.1007/s40314-021-01673-6

In this paper, we propose a new scheme for the temporal discretization of the new Caputo–Hadamard fractional derivative in the form of incomplete gmma function via Whittaker M function. We derive the truncation error for the new scheme. Hence, this discretization was used to solve numerically fractional ordinary differential equation and fractional partial differential equation in the Caputo–Hadamard sense for the order, α ∈ ( 0 , 1 ) . The numerical results show that the method is highly effective and efficient.