The diamond-alpha Riemann integral and mean value theorems on time scales

Abstract

We study diamond-alpha integrals on time scales. A diamond-alpha version of Fermat's theorem for stationary points is also proved, as well as Rolle's, Lagrange's, and Cauchy's mean value theorems on time scales.

14 pages

References in corpus (2)

• Diamond-$\alpha$ Jensen's Inequality on Time Scales
• Diamond-alpha Polynomial Series on Time Scales

Cited by in corpus (14)

• A Fractional Calculus on Arbitrary Time Scales: Fractional Differentiation and Fractional Integration
• Fractional calculus of variations for a combined Caputo derivative
• Transversality Conditions for Infinite Horizon Variational Problems on Time Scales
• Noether's symmetry theorem for nabla problems of the calculus of variations
• Higher-order Hahn's quantum variational calculus
• The Riemann-Stieltjes integral on time scales
• Nonsymmetric and Symmetric Fractional Calculi on Arbitrary Nonempty Closed Sets
• A symmetric quantum calculus
• A Study of Diamond-alpha dynamic equations on regular time scales
• Fractional Calculus on Time Scales
• Combined Delta-Nabla Sum Operator in Discrete Fractional Calculus
• Existence of Three Positive Solutions to Some $p$-Laplacian Boundary Value Problems
• L'Hopital-Type Rules for Monotonicity with Application to Quantum Calculus
• Time Scales and Mathematica