Analytical treatment of system of Abel integral equations by Homotopy analysis method

Jafarian A., Ghaderi P., Khalili Golmankhaneh A., Baleanu D.

Romanian Reports in Physics, cilt.66, sa.3, ss.603-611, 2014 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 66 Sayı: 3
  • Basım Tarihi: 2014
  • Dergi Adı: Romanian Reports in Physics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.603-611
  • Anahtar Kelimeler: Fractional calculus, H-curve, Homotopy analysis method, System of Abel integral equations
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

Abel equation has important applications in describing the least time for an object which is sliding on surface without friction in uniform gravity, and the classical theory of elasticity of materials is modeled by a system of Abel integral equations. In this manuscript, the homotopy analysis method is presented for obtaining analytical solutions of a system of Abel integral equations as fractional equations. The applied method has lessened the size of calculation and improved the accuracy of solution in the case of the singular Abel integral equation. The illustrated examples and numerical results have proved the assertion.