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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Different forms of solution were presented depending on the values of the parameter appeared in the problem.
📌 3 Key Takeaways
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Objective & Hypothesis:In this work, we consider a number of boundary-value problems for time-fractional heat equation with the recently introduced Caputo-Fabrizio derivative.
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Key Findings & Data:Using the method of separation of variables, we prove a unique solvability of the stated problems.
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Conclusion & Impact:Different forms of solution were presented depending on the values of the parameter appeared in the problem.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Caputo-Fabrizio fractional derivative · Caputo-Fabrizio fractional derivative
Abstract
In this work, we consider a number of boundary-value problems for time-fractional heat equation with the recently introduced Caputo-Fabrizio derivative. Using the method of separation of variables, we prove a unique solvability of the stated problems. Moreover, we have found an explicit solution to certain initial value problem for Caputo-Fabrizio fractional order differential equation by reducing the problem to a Volterra integral equation. Different forms of solution were presented depending on the values of the parameter appeared in the problem.
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Cite This Article
Al-salti, N., Karimov, E., Kerbal, S. (2016). Boundary-value problems for fractional heat equation involving Caputo-Fabrizio derivative. New Trends in Mathematical Sciences, Cilt: 4 Sayı: 4, 79–89. https://ajindex.com/articles/1003786