Fractional Derivatives and Leibniz Rule

From MaRDI portal
Publication:5619259

DOI10.2307/2316573zbMath0216.09303OpenAlexW4234036316WikidataQ123153747 ScholiaQ123153747MaRDI QIDQ5619259

Thomas J. Osler

Publication date: 1971

Published in: The American Mathematical Monthly (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2316573




Related Items (33)

Generalizations of fractional \(q\)-Leibniz formulae and applicationsRadii of starlikeness and convexity of $q-$Mittag--Leffler functionsSome relations involving generalized Hurwitz-Lerch zeta function obtained by means of fractional derivatives with applications to Apostol-type polynomialsOn the fractional calculus of multivariate Mittag-Leffler functionsOn a more general fractional integration by parts formulae and applicationsAn expansion theorem involving \(H\)-function of several complex variablesScale calculus and the Schrödinger equationOn models of irreducible q- representations of sl(2, c)The use of fractional derivatives to expand analytical functions in terms of quadratic functions with applications to special functionsComplete and orthonormal sets of exponential-type orbitals with non-integer quantum numbersAssociation of variables inn-dimensional Laplace transformOn some new properties of fractional derivatives with Mittag-Leffler kernelLeibniz type rule: \(\psi\)-Hilfer fractional operatorA new glance on the Leibniz rule for fractional derivativesRemark on certain transformations for multiple hypergeometric functionsIntegral transform methods for solving fractional dynamic equations on time scalesAn elliptic regularity theorem for fractional partial differential operatorsTaylor-like expansion in terms of a rational function obtained by means of fractional derivativesA new transformation formula for fractional derivatives with applicationsFour derivations of an interesting bilateral series generalizing the series for zeta of 2On using random walks to solve the space-fractional advection-dispersion equationsComputation of certain infinite series of the form \(\sum f(n)n^k \) for arbitrary real-valued \(k\)Expansion formulas for an extended Hurwitz-Lerch zeta function obtained via fractional calculusDiscussion on the Leibniz rule and Laplace transform of fractional derivatives using series representationApplications of some fixed point theorems for fractional differential equations with Mittag-Leffler kernelThe Lerch zeta function as a fractional derivativeLocal fractional derivatives of differentiable functions are integer-order derivatives or zeroNew expansion formulas for a family of the \(\lambda\)-generalized Hurwitz-Lerch zeta functionsOn some further hypergeometric series identities obtained via fractional calculusA mathematical approach with fractional calculus for the modelling of children's physical developmentFractionalisation of complex d-bar derivativesFractional systems: theoretical foundationsFurther results involving a class of generalized Hurwitz-Lerch zeta functions




This page was built for publication: Fractional Derivatives and Leibniz Rule