A Truly Conformable Calculus on Time Scales
Benaoumeur Bayour, Ahmed Hammoudi, Delfim F. M. Torres
TL;DR
This paper introduces a new conformable derivative calculus on time scales, establishing its fundamental properties and solving linear differential equations, thus unifying continuous and discrete analysis.
Contribution
It presents the first definition of conformable derivatives on time scales and develops a comprehensive calculus framework for them.
Findings
Fundamental properties of conformable derivatives and integrals on time scales are established.
Solutions to linear conformable differential equations with constant coefficients are derived.
Hyperbolic and trigonometric functions are extended within this new calculus framework.
Abstract
We introduce the definition of conformable derivative on time scales and develop its calculus. Fundamental properties of the conformable derivative and integral on time scales are proved. Linear conformable differential equations with constant coefficients are investigated, as well as hyperbolic and trigonometric functions.
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Taxonomy
TopicsFractional Differential Equations Solutions · Differential Equations and Numerical Methods · Differential Equations and Boundary Problems