Mellin Transformation for Solving Fractional Diffusion Equations with Caputo-Fabrizio Derivative
0
조회
0
다운로드
2
인용
0
참고문헌
키워드
초록
This study solves a fractional diffusion equation with Caputo-Fabrizio derivative using the Mellin transfrom. We use the Mellin transform to simplify the equation and transform it into an ordinary differential equation. With the Mellin inversion, We have the solution of the governing equation. Then, We apply our solution to the example problem and investigate the approximations using the Taylor series and figures.
Abstract
This study solves a fractional diffusion equation with Caputo-Fabrizio derivative using the Mellin transfrom. We use the Mellin transform to simplify the equation and transform it into an ordinary differential equation. With the Mellin inversion, We have the solution of the governing equation. Then, We apply our solution to the example problem and investigate the approximations using the Taylor series and figures.
참고문헌 (8)
- Žecová M, "Heat conduction modeling by using frac-tional-order derivatives", Appl Math Comput, 257, pp.365~373 (2015)
- Caputo M, "A new definition of fractional derivative without singular kernel", Progr Fract Differ Appl, 1, pp.74~85 (2015)
- Mozyrska D, "Solutions of systems with the Caputo-Fabrizio fractional delta derivative on time scales", Nonlinear Anal-Hybri, 32, pp.168~176 (2019)
- Baleanu D, "A fractional differential equation model for the COVID-19 transmission by using the Caputo-Fabrizio derivative", Adv Differ Equ-Ny, pp.299~ (2020)
- Azhar N, "Solution of fuzzy fractional order differential equations by fractional Mellin transform method", J Comput Appl Math, 400, pp.113727~ (2022)
- Tuan NH, "Well-posedness of an initial value problem for fractional diffusion equation with Caputo-Fabrizio derivative", J Comput Appl Math, 325, pp.112811~ (2020)
- Losada J, "Properties of a new fractional derivative without singluar kernal", Progr Fract Differ Appl, 1, pp.1~13 (2015)
- Iwaniec H, "Analytic number theory" (2004), American Mathematical Society