A novel exact solution for the fractional Ambartsumian equation

Abstract Fractional calculus (FC) is useful in studying physical phenomena with memory effect. In this paper, a fractional form of Ambartsumian equation considered utilizing the Caputo derivative. The Heaviside expansion formula classical (CC) extended/developed view FC. Then, extended applied to obtain exact solution simplest form. Several theorems and lemmas are proved facilitate evaluation inverse Laplace transform specific expressions forms. established terms one-parameter Mittag-Leffler function which provided for first time present reduces corresponding one relevant literature as order tends one. Moreover, convergence obtained theoretically proved. Comparisons another approach performed. advantage analysis over existing discussed analyzed.