Fuge`re, "The use of fractional derivatives to expand analytical functions in terms of quadratic functions with applications to special functions," Applied Mathematics and Computation, vol. 187, no. 1, pp. 507-
Special Functions in Fractional Calculus and Related Fractional Differintegral EquationsThe subject of fractional calculus (that is, calculus of integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance during the past four decades, due mainly to ...
Fractional derivatives and special functions SIAM Rev., 18 (1976), pp. 240-268 Google Scholar [13] V. Kiryakova All the special functions are fractional differintegrals of elementary functions J. Physics A: Math. & Gen., 30 (1997), pp. 5085-5103 View in ScopusGoogle Scholar [14] V....
Fractional derivativesExtended Special functionsRecently an extended operator of fractional derivative related to a generalized beta function has been used in order to obtain some generating relations involving extended hypergeometric functions [19]. In this paper, an extended fractional derivative operator ...
Section 2 formulates the F-BCCM and the mathematical concept of fractional order Caputo derivative (F-CD). Section 3 discusses the shifted Legendre polynomials (SLP), as well as the GSLP and its operational matrix of derivatives and function approximation. Section 4 addresses the convergence ...
E. Second-order approximations for variable order fractional derivatives: Algorithms and applications. J. Comput. Phys. 293, 184–200. https://doi.org/10.1016/j.jcp.2014.08.015 (2015). Article ADS MathSciNet Google Scholar Diaz, G. & Coimbra, C. F. M. Dynamics and control of ...
Q6 We know that is geometrically interpreted as the slope of the curve and gives us the concavity of the curve. But the third and higher derivatives give us little or no geometric information. Since these are special cases of we are not surprised that there is no easy geometric meaning for...
Integral Transforms and Special FunctionsH. Srivastava, S. Yakubovich, and Y.F. Luchko, The convolution method for the development of new Leibniz rules involving fractional derivatives and of their integral analogues, Integral Transform Spec. Funct. 1 (1993), pp. 119-134....
On Some Inequalities Involving Liouville–Caputo Fractional Derivatives and Applications to Special Means of Real NumbersLiouville–CaputofractionalderivativeconvexityDragomir–AgarwalinequalityWe are concerned with the class of functions f ∈ C 1 ( [ a , b ] ; R ) , a , b ∈ R , a b , such...
[34,35] developed a fractional model of tumor-immune system interaction related to lung cancer and also studied the interactions between COVID-19 and diabetes with hereditary traits using real data. Naik et al. [36] analyzed COVID-19 epidemics with treatment in fractional derivatives on the ...