Applications of Structural Nabla Derivatives on Time Scales to Dynamic Equations

Abstract

We present here more general concepts of Hausdorff derivatives (structural Nabla derivatives) on a timescale. We examine structural Nabla integration on temporal scales. Using the fixed-point theorem, we establish adequate criteria for the question of existence and uniqueness of the solution to an initial value problem characterized by structural Nabla derivatives on timescales. Furthermore, some features of the new operator are proven and illustrated by using concrete examples.

Keywords

• Hausdorff derivative
• existence
• structural and fractal derivatives
• self-similarity
• fractional derivatives
• timescales