We shall investigate the inflation for the D-brane model, motivated by the modified gravity \(F(\phi ,T)\) . This gravity has been recently introduced in the literature. The feasibility of the D-brane inflation theory in the \(F(\phi ,T)\) -gravity has been studied in conjunction with the most recent Planck data. We shall analyze the slow-roll inflation in the context of the \(F(\phi )T\) -gravity, via the D-brane model. Then, we shall calculate the inflation dynamics to obtain the scalar spectral index “ \(n_s\) ” and the tensor-to-scalar ratio “r”. Besides, we investigate the dynamics of the reheating for this model. Our model accurately covers the left-hand side of the Planck data and the D-brane inflation.
