A semi-analytical solutions of fractional Riccati's differential equation via singular and non-singular operators

Abstract

Looking for offer a solution of the  Riccati's differential equations of fractional order (FRDEs) involving Caputo derivative (CD), Caputo-Fabrizio derivative (CFD) or Atangana-Baleanu  derivative (ABD) in this comparative research is based on  a semi-analytical iterative approach. Temimi and  Ansari  introduced this method and called it  TAM. The comparison of the time used in minutes is given for three derivatives  CD,  CFD  and  ABD. Meanwhile, the comparison of the approximate solutions with  CD, CFD and ABD  are presented. Regarding the help of the  software  Mathematica, all the results have been obtained and the calculations have been done.