The core objective of this study is to develop a hybrid of homotopy perturbation transform method along with Atangana Baleanu Caputo operator for determination of numerous linear and nonlinear convection-diffusion problems arising in physical phenomena. The homotopy perturbation transform methodology is a bland of homotopy perturbation transform method and Laplace transform method. The nonlinear terms can be easily handled by the use of He’s polynomials but we tried to utilize Atangana Baleanu Caputo operator (ABC-operator) to change the potency of conversion of series result. The approach helps in nursing improvement in the methodology to resolve many sorts of partial differential equations. The approximate solutions obtained by the projected theme in an exceedingly big selection of the problems domain were compared with those results obtained from the particular solutions. The comparison shows an explicit agreement between the results.

Keywords: Atangana Baleanu Caputo operator, Convection-diffusion, Homotopy perturbation transform method, Laplace transform.