On a new modified fractional analysis of Nagumo equation

Saad K. M., Deniz S., Baleanu D.

International Journal of Biomathematics, cilt.12, sa.3, 2019 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 12 Sayı: 3
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1142/s1793524519500347
  • Dergi Adı: International Journal of Biomathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Atangana-Baleanu-Caputo time-fractional derivatives, Caputo-Fabrizio-Caputo derivative, homotopy analysis transform method, Nagumo equation, nonlinear diffusion and convection
  • Manisa Celal Bayar Üniversitesi Adresli: Hayır

Özet

In this work, a new modified fractional form of the Nagumo equation has been presented and deeply analyzed. Using the Caputo-Fabrizio and Atangana-Baleanu time-fractional derivatives, classical Nagumo model is transformed to a new fractional version. The modified equation has been solved by using the homotopy analysis transform method. The convergence analysis has been also examined with the help of the so-called h-curves and average residual error. Comparing the obtained approximate solution with the exact solution leaves no doubt believing that the proposed technique is very efficient and converges toward the exact solution very rapidly.