A general quantum difference calculus

DOI10.1186/s13662-015-0518-3zbMath1422.39010OpenAlexW1545895872WikidataQ59431040 ScholiaQ59431040MaRDI QIDQ1620743

Enas M. Shehata, Abdel-Shakoor M. Sarhan, Alaa E. Hamza, Khaled A. Aldwoah

Publication date: 13 November 2018

Published in: Advances in Difference Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13662-015-0518-3

zbMATH Keywords

quantum calculusHahn difference operatorJackson \(q\)-difference operatorquantum difference operator

Mathematics Subject Classification ID

Additive difference equations (39A10) Difference operators (39A70) Difference equations, scaling ((q)-differences) (39A13) Linear difference operators (47B39)

Related Items (15)

On the fixed points of certain types of functions for constructing associated calculi ⋮ A general quantum Laplace transform ⋮ Variations around a general quantum operator ⋮ Asymptotic iteration method for solving Hahn difference equations ⋮ A \(\beta\)-convolution theorem associated with the general quantum difference operator ⋮ q−Hamiltonian systems ⋮ Hermite-Hadamard inequalities for quantum integrals: a unified approach ⋮ On a class of difference operator and its applications to a family of analytic functions ⋮ Theory of \(n\)th-order linear general quantum difference equations ⋮ Unnamed Item ⋮ Leibniz’s Rule and Fubini’s Theorem Associated with a General Quantum Difference Operator ⋮ Aβ-Sturm–Liouville problem associated with the general quantum operator ⋮ Quantum exponential functions in a Banach algebra ⋮ \(q\)-non uniform difference calculus and classical integral inequalities ⋮ Existence results of nonlocal Robin mixed Hahn and \(q\)-difference boundary value problems

Cites Work

• Unnamed Item
• \(q\)-fractional calculus and equations
• The Hahn quantum variational calculus
• Functional analysis in modern applied mathematics
• Existence and uniqueness of solutions of Hahn difference equations
• Quantum calculus on finite intervals and applications to impulsive difference equations
• Hahn difference operator and associated Jackson-Nörlund integrals
• The power quantum calculus and variational problems
• Über Orthogonalpolynome, die q‐Differenzengleichungen genügen
• Quantum calculus

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