Exclusive semileptonic decays of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>D</mml:mi></mml:mrow></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml

Semileptonic decays of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>D</a:mi></a:math> and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>D</c:mi><c:mi>s</c:mi></c:msub></c:math> mesons into orbitally and radially excited strange and light mesons are studied in detail within the framework of the relativistic quark model based on the quasipotential approach and quantum chromodynamics. The hadronic matrix elements of the weak current between meson states are calculated with the consistent account of relativistic effects including contributions of the intermediate negative energy states and boosts of the meson wave functions from the rest to moving reference frame. The invariant form factors that parametrize these matrix elements are obtained as the overlap integrals of the initial and final meson wave functions. Their dependence on the square of the transferred momentum <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msup><e:mi>q</e:mi><e:mn>2</e:mn></e:msup></e:math> is explicitly determined within the whole accessible kinematic range. A convenient analytical approximation for numerical values of form factors is given. These form factors and helicity formalism are employed for the calculation of the differential and total semileptonic decay rates of charm mesons into excited strange and light mesons. Different asymmetry and polarization parameters are also evaluated. The obtained results are compared with other theoretical calculations and available experimental data. Reasonable agreement with experimentally measured semileptonic decay branching fractions and upper bounds is obtained.