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

Yıl 2016, Cilt: 4 Sayı: 4, 79 - 89, 31.12.2016

Nasser Al-salti Erkinjon Karimov Sebti Kerbal

Öz

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.

Anahtar Kelimeler

Caputo-Fabrizio fractional derivative

Kaynakça

• M.Caputo and M.Fabrizio. A new definition of fractional derivative without singular kernel. Progr. Fract. Differ. Appl. 1, No 2, 73–85 (2015)
• M.Caputo and M.Fabrizio. Applications of new time and spatial fractional derivatives with exponential kernels. Progr. Fract. Differ. Appl. 2, No 1, 1–11 (2016)
• J. Losada and J.J. Nieto. Properties of a new fractional derivative without singular kernel. Progr. Fract. Differ. Appl. 1, No 2, 87–92 (2015)
• A.Atangana. On the new fractional derivative and application to nonlinear Fisher’s reaction-diffusion equation. Applied Mathematics and Computation 273 (2016) 948–956.
• Xiao-Jun Yang, H.M.Srivastava, J.A.Machado Tenreiro. A new fractional derivative without singular kernel: Application to the modelling of the steady heat flow, 2015, DOI:10.2298/TSCI151224222Y
• 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)
• 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)
• 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.