  Motivated by earlier works on reconstruction of modified gravity models with
dark energy components, we extend them by considering a newly proposed model of
(m, n)- type of holographic dark energy for two models of modified gravity,
f(R) and f(T) theories, where R and T represent Ricci scalar and torsion scalar
respectively. Specifically we reconstruct the two later gravity models and
discuss their viability and cosmography. The obtained gravity models are ghost
free, compatible with local solar system tests and describe effective positive
gravitational constant.
