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In the present article, we investigate the physical acceptability of the spatially homogeneous and isotropic Friedmann–Lemâitre–Robertson–Walker line element filled with two fluids, with the first being pressureless matter and the second being different types of holographic dark energy. This geometric and material content is considered within the gravitational field equations of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>T</mi><mo>,</mo><mi>B</mi><mo>)</mo></mrow></semantics></math></inline-formula> (where <i>T</i> is the torsion scalar and the <i>B</i> is the boundary term) gravity in Hubble’s cut-off. The cosmological parameters, such as the Equation of State (EoS) parameter, during the cosmic evolution, are calculated. The models are stable throughout the universe expansion. The region in which the model is presented is dependent on the real parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula> of holographic dark energies. For all <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>δ</mi><mo>≥</mo><mn>4.5</mn></mrow></semantics></math></inline-formula>, the models vary from <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Λ</mo></semantics></math></inline-formula>CDM era to the quintessence era.