Abstract
In this paper, we have considered two different sub-diffusion equations involving Hilfer, hyper-Bessel and Erdélyi-Kober fractional derivatives. Using a special transformation, we equivalently reduce the considered boundary value problems for fractional partial differential equation to the corresponding problems for ordinary differential equation. An essential role is played by certain properties of Erdélyi-Kober integral and differential operators. We have applied also successive iteration method to obtain self-similar solutions in an explicit form. The obtained self-similar solutions are represented by generalized Wright type function. We have to note that the usage of imposed conditions is important to present self-similar solutions via given data.
Original language | English |
---|---|
Pages (from-to) | 16-27 |
Number of pages | 12 |
Journal | International Journal of Optimization and Control: Theories and Applications |
Volume | 11 |
Issue number | 3 |
DOIs | |
Publication status | Published - 2021 |
Keywords
- Erdélyi-Kober fractional derivative
- Hilfer derivatives
- Hyper-Bessel operator
- Self-similar solution
- Successive iteration method
ASJC Scopus subject areas
- Control and Optimization
- Applied Mathematics