Fractional q-Calculus on a time scale

From MaRDI portal

Publication:3607660

Jump to:navigation, search

DOI10.2991/jnmp.2007.14.3.4zbMath1157.81315OpenAlexW2137546828MaRDI QIDQ3607660

F. Merdivenci Atici, Paul W. Eloe

Publication date: 26 February 2009

Published in: Journal of Nonlinear Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2991/jnmp.2007.14.3.4

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50)

Related Items (93)

\(Iq\)-calculus and \(Iq\)-Hermite-Hadamard inequalities for interval-valued functions ⋮ Inflation driven by \(q\)-de Sitter ⋮ On a discrete fractional three-point boundary value problem ⋮ New applications of the variational iteration method -- from differential equations to \(q\)-fractional difference equations ⋮ An increasing variables singular system of fractional \(q\)-differential equations via numerical calculations ⋮ On a fractional \(q\)-differential inclusion on a time scale via endpoints and numerical calculations ⋮ On four-point fractional \(q\)-integrodifference boundary value problems involving separate nonlinearity and arbitrary fractional order ⋮ On a system of fractional \(q\)-differential inclusions via sum of two multi-term functions on a time scale ⋮ Caputo type fractional difference operator and its application on discrete time scales ⋮ Analytical solutions of \(q \)-fractional differential equations with proportional derivative ⋮ Certain fractional \(q\)-symmetric integrals and \(q\)-symmetric derivatives and their application ⋮ Solvability of a \(q\)-fractional integral equation arising in the study of an epidemic model ⋮ On the oscillation of \( q\)-fractional difference equations ⋮ Fractional \(q\)-symmetric calculus on a time scale ⋮ Weighted bounded solutions for a class of nonlinear fractional equations ⋮ New approach to solutions of a class of singular fractional \(q\)-differential problem via quantum calculus ⋮ Existence of solutions for a system of singular sum fractional \(q\)-differential equations via quantum calculus ⋮ Existence and uniqueness of positive and nondecreasing solutions for a class of fractional boundary value problems involving the \(p\)-Laplacian operator ⋮ Positive solutions for boundary value problems of fractional difference equations depending on parameters ⋮ A generalized \(q\)-fractional Gronwall inequality and its applications to nonlinear delay \(q\)-fractional difference systems ⋮ On a nonlinear sequential four-point fractional \(q\)-difference equation involving \(q\)-integral operators in boundary conditions along with stability criteria ⋮ A fractional \(q\)-integral operator associated with a certain class of \(q\)-Bessel functions and \(q\)-generating series ⋮ Well-posed conditions on a class of fractional \(q\)-differential equations by using the Schauder fixed point theorem ⋮ Positive solutions for eigenvalue problems of fractional \(q\)-difference equation with \(\varphi\)-Laplacian ⋮ Fractional time-scales Noether theorem with Caputo \(\Delta\) derivatives for Hamiltonian systems ⋮ The solution theory of the nonlinear \(q\)-fractional differential equations ⋮ Coupled systems of Caputo type fractional \(\Delta\)-difference boundary value problems at resonance ⋮ Existence of solutions of boundary value problems for singular fractional \(q\)-difference equations ⋮ Existence results to positive solutions of fractional BVP with \(q\)-derivatives ⋮ Existence of solutions for a class of the boundary value problem of fractional \(q\)-difference inclusions ⋮ Fractional integro-differential calculus and its control-theoretical applications. I: Mathematical fundamentals and the problem of interpretation ⋮ Some new fractional \(q\)-integral Grüss-type inequalities and other inequalities ⋮ Twin iterative positive solutions of fractional \(q\)-difference Schrödinger equations ⋮ Substantiation of a quadrature-difference method for solving integro-differential equations with derivatives of variable order ⋮ Existence of positive solutions of nonlinear fractional \(q\)-difference equation with parameter ⋮ The existence of solutions to a class of boundary value problems with fractional difference equations ⋮ On existence of positive solutions for a class of discrete fractional boundary value problems ⋮ An efficient numerical method for \(q\)-fractional differential equations ⋮ Asymptotic behavior of solutions of fractional nabla \(q\)-difference equations ⋮ Dynamical analysis of a fractional discrete-time vocal system ⋮ Hahn Laplace transform and its applications ⋮ One dimensional fractional frequency Fourier transform by inverse difference operator ⋮ The existence of solutions to a system of discrete fractional boundary value problems ⋮ A computation method of Hausdorff distance for translation time scales ⋮ Existence, uniqueness, and controllability for Hilfer differential equations on times scales ⋮ Some new fractional quantum integral inequalities ⋮ Unique iterative solution for high-order nonlinear fractional \(q\)-difference equation based on \(\psi-(h,r)\)-concave operators ⋮ A generalized \(q\)-Mittag-Leffler function by \(q\)-Caputo fractional linear equations ⋮ \(q\)-Mittag-Leffler stability and Lyapunov direct method for differential systems with \(q\)-fractional order ⋮ Lebesgue regularity for nonlocal time-discrete equations with delays ⋮ New concepts of fractional Hahn's \(q,\omega \)-derivative of Riemann-Liouville type and Caputo type and applications ⋮ The \(q\)-fractional analogue for Gronwall-type inequality ⋮ A DIFFERENCE METHOD FOR SOLVING THE NONLINEAR q-FRACTIONAL DIFFERENTIAL EQUATIONS ON TIME SCALES ⋮ Stabilization of Fractional Order Discrete Chaotic Systems ⋮ On nonnegative solutions of fractional \(q\)-linear time-varying dynamic systems with delayed dynamics ⋮ A survey of recent results for the generalizations of ordinary differential equations ⋮ Three-point boundary value problems with delta Riemann-Liouville fractional derivative on time scales ⋮ Existence of three positive solutions for a class of boundary value problems of Caputo fractional \(q\)-difference equation ⋮ Unnamed Item ⋮ A discrete fractional Gronwall inequality ⋮ Positive solutions for a class of singular boundary value problems with fractional \(q\)-difference equations ⋮ Fractional quantum integral inequalities ⋮ Unnamed Item ⋮ Discrete Mittag-Leffler functions in linear fractional difference equations ⋮ A study of nonlinear fractional \(q\)-difference equations with nonlocal integral boundary conditions ⋮ On the \(q\)-Laplace transform and related special functions ⋮ A difference method for solving the \(q\)-fractional differential equations ⋮ Nonsymmetric and symmetric fractional calculi on arbitrary nonempty closed sets ⋮ Existence of multiple positive solutions for \(m\)-point fractional boundary value problems with \(p\)-Laplacian operator on infinite interval ⋮ Existence and uniqueness of positive solutions for three-point boundary value problem with fractional \(q\)-differences ⋮ Successive iteration and positive solutions for boundary value problem of nonlinear fractional \(q\)-difference equation ⋮ Initial value problems in discrete fractional calculus ⋮ Positive solutions of nonlinear boundary value problems for delayed fractional \(q\)-difference systems ⋮ Boundary value problems for fractional \(q\)-difference equations with nonlocal conditions ⋮ Existence results for fractional \(q\)-difference equations of order \(\alpha\in2,3[\) with three-point boundary conditions] ⋮ Unnamed Item ⋮ Synchronization of fractional-order discrete-time chaotic systems by an exact delayed state reconstructor: application to secure communication ⋮ Ulam stability of Caputo \(q\)-fractional delay difference equation: \(q\)-fractional Gronwall inequality approach ⋮ Positive solutions of nonlocal boundary value problem for high-order nonlinear fractional \(q\)-difference equations ⋮ The existence of nonnegative solutions for a nonlinear fractional \(q\)-differential problem via a different numerical approach ⋮ Existence and uniqueness of solution for a nonhomogeneous discrete fractional initial value problem ⋮ Positive solutions for singular boundary value problem with fractional \(q\)-differences ⋮ SUCCESSIVE ITERATIONS FOR UNIQUE POSITIVE SOLUTION OF A NONLINEAR FRACTIONAL Q-INTEGRAL BOUNDARY VALUE PROBLEM ⋮ \(\Delta\)-Choquet integral on time scales with applications ⋮ Fractional calculus on time scales with Taylor's theorem ⋮ Existence of positive solutions to a higher order singular boundary value problem with fractional \(q\)-derivatives ⋮ On multi-step methods for singular fractional \(q\)-integro-differential equations ⋮ THE UNIQUE EXISTENCE OF SOLUTION IN THE q-INTEGRABLE SPACE FOR THE NONLINEAR q-FRACTIONAL DIFFERENTIAL EQUATIONS ⋮ Cauchy problem for a class of fractional differential equations on time scales ⋮ Solutions of two fractional \(q\)-integro-differential equations under sum and integral boundary value conditions on a time scale ⋮ Existence and uniqueness of solutions for a nonlinear coupled system of fractional differential equations on time scales ⋮ Positive solution for \(q\)-fractional four-point boundary value problems with \(p\)-Laplacian operator ⋮ The Poisson distribution, abstract fractional difference equations, and stability

Cites Work

This page was built for publication: Fractional q-Calculus on a time scale

Retrieved from "https://portal.mardi4nfdi.de/w/index.php?title=Publication:3607660&oldid=17037307"