On self-similar solutions of time and space fractional sub-diffusion equations

Fatma Al-Musalhi*, Erkinjon Karimov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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 languageEnglish
Pages (from-to)16-27
Number of pages12
JournalInternational Journal of Optimization and Control: Theories and Applications
Issue number3
Publication statusPublished - 2021


  • Erdélyi-Kober fractional derivative
  • Hilfer derivatives
  • Hyper-Bessel operator
  • Self-similar solution
  • Successive iteration method

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics

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