Quintessence behaviour dark energy models in f(Q,B)-gravity theory with observational constraints

The present paper is an investigation of dark energy scenarios of cosmological models in recently proposed modified non-metricity gravity theory with boundary term in a flat FLRW spacetime universe. We have considered an arbitrary function $f(Q,B)=\alpha Q^2+\beta B^2$, where $Q$ is the non-metricity scalar, $B$ is the boundary term given by $B=\mathring{R}-Q$, and $\alpha ,\beta$ are the model parameters, which is quadratic in both $Q$ and $B$, for the action. We have investigated the dark energy features of the model with observational constraints on an specific Hubble function $H\left(z\right)=H_0{[\lambda {(1+z)}^n+k]}^{\frac{1}{2}}$, where $H_0$ is present value of Hubble constant, $n,k,\lambda$ are arbitrary parameters with $\lambda +k=1$. We have found a transit phase (decelerated in past and accelerated at present) expanding universe model and have found the behaviour of dark energy equation of state (EoS) ${\omega }^{\left(de\right)}$ as $(-1.007\le {\omega }^{\left(de\right)}\le -\frac{1}{3})$ and Om diagnostic analysis of the model shows the quintessence behaviour at present and cosmological constant scenario at late-time universe. We have also, analysed the statefinder parameters for the classification of dark energy models during expansion and also, we have estimated the present age of the universe that are found very closed to the recent observations.