Approximation of complex functions from Lebesgue space with variable exponent L^p(.) (Γ) on Dini smooth curves (Latakia University Journal -Basic Sciences Series, 2018)
.In this research, we have studied some of the new properties of the fractional modulus of smoothness defined by the researcher Akgun in 2011. Then we have investigated the direct problem of approximation theory of complex functions from Lebesgue spaces with variable exponent  on Dini smooth curves by rational functions related to Faber polynomials using fractional modulus of smoothness. We have obtained approximation of analytic functions from Smirnov class with variable exponent  on a simply connected domain  bounded by Dini smooth curve using fractional modulus of smoothness. It should be noted that in 2016, both researchers Israfilov and Testici studied approximation of functions from  on Dini smooth curves using modulus of smoothness identifier with the following relation:.