We have to note that the usage of imposed conditions is important to present self-similar solutions via given data.
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper, we have considered two different sub-diffusion equations involving Hilfer, hyper-Bessel and Erd´elyi-Kober fractional derivatives.
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Key Findings & Data: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.
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Conclusion & Impact:We have to note that the usage of imposed conditions is important to present self-similar solutions via given data.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
In this paper, we have considered two different sub-diffusion equations involving Hilfer, hyper-Bessel and Erd´elyi-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 Erd´elyi-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.
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Cite This Article
AL-MUSALHİ, F., KARIMOV, E. (2022). On self-similar solutions of time and space fractional sub-diffusion equations. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), Cilt: 11 - Sayı: 3, 16–27. https://ajindex.com/articles/440553
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