JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, cilt.366, 2020 (SCI-Expanded)
We present q-analogues of exponential Euler polynomials and Euler-Frobenius polynomials from B-splines with knots both at q-integers and in geometric progression. We also investigate the relations between q-Eulerian numbers, q-Eulerian polynomials, q-Euler-Frobenius polynomials and B-splines. We derive q-Euler-Frobenius polynomials using q-analogue of exponential splines. It is shown that B-splines with knots at q-integers and B-splines with knots in geometric progression have same values on their knot points. We also construct a q-analogue of Worpitzky identity. (C) 2019 Elsevier B.V. All rights reserved.