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Dergiler / New Trends in Mathematical Sciences / 2016 / Cilt: 4 Sayı: 4

Boundary-value problems for fractional heat equation involving Caputo-Fabrizio derivative

Nasser Al-salti(Sultan Qaboos University, Al-Khoud, Muscat)
Erkinjon Karimov(Sultan Qaboos University)
Sebti Kerbal(Sultan Qaboos University)
Sayfa
79–89
Yayın Tarihi
2016-12-31
DOI
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Different forms of solution were presented depending on the values of the parameter appeared in the problem.

📌 3 Maddede Bu Makale

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Amaç & Hipotez: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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Temel Bulgular & Veri:Using the method of separation of variables, we prove a unique solvability of the stated problems.
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Sonuç & Katkı:Different forms of solution were presented depending on the values of the parameter appeared in the problem.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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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Bu Makaleye Atıf Yap

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

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Kaynakça (8)

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  6. A.Atangana, D.Baleanu. New fractional derivative with nonlocal and non-singular kernel: Theory and application to hest transfer model. Thermal Science 2016. Online-First Issue 00, Pages 18-18, doi:10.2298/TSC1160111018A(2016)
  7. A.Atangana, I.Koca. Chaos in a simple nonlinear system with Atangana-Baleanu derivatives with fractional order. Chaos, Solitons and Fractals, http://dx.doi.org/10.1016/j.chaos.2016.02.012 (2016)
  8. V.A. Il’in. Existence of a Reduced System of Eigen- and Associated Functions for a Nonself adjoint Ordinary Differential Operator. Trudy MIAN. 142 (1976) 148–155.