Abstract

The aim of this chapter is to find solutions for systems of nonlinear fractional-order differential equations arising in a helium-burning network using the q-homotopy analysis transform method (q-HATM). We consider a model that illustrates the chemical reactions involved in a helium-burning network. The Atangana–Baleanu (AB) operator with fractional order and associated algorithm considered here is an elegant consolidation of Laplace transform with q-HAM. The existence and uniqueness of the fixed-point concept is illustrated, as is the competence of the projected algorithm. The physical nature of the results obtained has been plotted in a different arbitrary order. The results confirm that the algorithm is very effective, highly methodical and easy to apply, and the fractional differential system associated with allied scientific disciplines can be accurately inspected.