TY - JOUR
T1 - On self-similar solutions of time and space fractional sub-diffusion equations
AU - Al-Musalhi, Fatma
AU - Karimov, Erkinjon
N1 - Publisher Copyright:
© 2021 Balikesir University. All rights reserved.
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
KW - Erdélyi-Kober fractional derivative
KW - Hilfer derivatives
KW - Hyper-Bessel operator
KW - Self-similar solution
KW - Successive iteration method
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U2 - 10.11121/IJOCTA.2021.1065
DO - 10.11121/IJOCTA.2021.1065
M3 - Article
SN - 2146-0957
VL - 11
SP - 16
EP - 27
JO - International Journal of Optimization and Control: Theories and Applications
JF - International Journal of Optimization and Control: Theories and Applications
IS - 3
ER -