Maryam Shahsavari - Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, P. O. Box ۳۵۱۹۵-۳۶۳, Semnan, Iran.
Leila Torkzadeh - Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, P. O. Box ۳۵۱۹۵-۳۶۳, Semnan, Iran.
Kazem Nouri - Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, P. O. Box ۳۵۱۹۵-۳۶۳, Semnan, Iran.

In this article, a numerical method is presented to solve Abel’s equations. In the given method, the solution of the equation is found as a finite expansion of the shifted Legendre polynomials. To this end, the integral and differential parts of the equation are converted to vector-matrix representations. Therefore, the equation is converted to an algebraic system of the equations and by solving it, the solution of the equation is obtained. Further, the numerical example is given to illustrate the method’s efficiency.

Abel’s equation, Integral equation, Caputo differential operator, Shifted Legendre polynomial