Approximation of fractional derivatives by Brass-Stancu operators

Başcanbaz-Tunca, Gülen; Erençin, Ayşegül; Feza Güvenilir, A.; Păltănea, Radu

doi:10.2478/auom-2025-0016

Abstract

In this paper, we study uniform approximation of fractional derivatives in Caputo sense by Brass-Stancu operators. For the rate of approximation, we give some estimates in terms of the modulus of continuity.

References

O. Agratini, Application of divided differences to the study of monotonicity of a sequence of D.D. Stancu polynomials, Rev. Anal. Numér. Théor. Approx., 25 (1996), nos, 1–2, 3–10.
Search in Google Scholar Back to article
G. Anastassiou, Fractional Korovkin theory, Chaos, Solitons & Fractals, 42(4), (2009), 2080–2094.
Search in Google Scholar Back to article
G. Anastassiou, Fractional Voronovskaya type asymptotic expansions for quasi-interpolation neural network operators, Cubo, 14(3) (2012), 71–83.
Search in Google Scholar Back to article
H. Brass, Eine Verallgemeinerung der Bernsteinschen Operatoren, Abh. Math. Sem.Univ. Hamburg, 36 (1971), 111–122.
Search in Google Scholar Back to article
T. Bostancı, G. Başcanbaz-Tunca, On Stancu operators depending on a non-negative integer, Filomat, 36(18) (2022), 6129–6138.
Search in Google Scholar Back to article
M. Cantarini, D. Costarelli, G. Vinti, Approximation results in Sobolev and fractional Sobolev spaces by sampling Kantorovich operators, Frac. Calc. Appl. Anal., 26 (2023), 2493–2521.
Search in Google Scholar Back to article
M. Caputo, Linear model of dissipation whose Q is almost frequency independent-II, Geophys. J. Roy. Astr. S., 13(5) (1967), 529–539.
Search in Google Scholar Back to article
A. Chirilă, M. Marin, The theory of generalized thermoelasticity with fractional order strain for dipolar materials with double porosity, J. Mater. Sci., 53, (2018), 3470–3482.
Search in Google Scholar Back to article
K. Diethelm, The Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type, Lecture Notes in Mathematics, Springer-Verlag, Berlin Heildeberg, 2010.
Search in Google Scholar Back to article
H. H. Gonska, On the composition and decomposition of positive linear operators, in: Kovtunets, V. V. (ed.) et al., Approximation Theory and its Applications. Proc. int. conf. ded. to the memory of Vl. K. Dzyadyk, Kiev, Ukraine, May 27–31, 1999. Pr. Inst. Mat. Nats. Akad. Nauk Ukr., Mat. Zastos. 31 (2000), 161–180.
Search in Google Scholar Back to article
C. Ionescu, A. Lopes, D. Copot, J. A. T. Machado, J. H. T. Bates, The role of fractional calculus in modeling biological phenomena: a review, Commun. Nonlinear Sci. Numer. Simul. 51 (2017), 141–159.
Search in Google Scholar Back to article
H. Khosravian-Arab, D. F. M. Torres, Uniform approximation of fractional derivatives and integrals with application to fractional differential equations. Nonlinear Stud., 20(4) (2013), 533–548.
Search in Google Scholar Back to article
B. Mond, Note: On the degree of approximation by linear positive operators, J. Approx. Theory, 18 (1976), 304–306.
Search in Google Scholar Back to article
R. Păltănea, Approximation of fractional derivatives by Bernstein operators, Gen. Math., 22(1) (2014), 91–98.
Search in Google Scholar Back to article
D. D. Stancu, Approximation of functions by means of a new generalized Bernstein operator, Calcolo, 20(2) (1983), 211–229.
Search in Google Scholar Back to article
V. E. Tarasov (Ed.) Mathematical Economics: Application of fractional calculus, MDPI, Basel, 2020.
Search in Google Scholar Back to article
Lianying Yun, Xueyan Xiang, On shape-preserving properties and simultaneous approximation of Stancu operator, Anal. Theory Appl., 24(2) (2008), 195–204.
Search in Google Scholar Back to article

Approximation of fractional derivatives by Brass-Stancu operators

Abstract

Paradigm

My account