Tatyana A. Komleva, Andrej V. Plotnikov, Natalia V. Skripnik

Solution of the Cauchy Problem for Impulsive Linear Set-Valued Differential Equations with a Conformable Fractional-Fractal Derivative

abstract:
The article presents a conformal fractional-fractal derivative for set-valued mappings, unifying conformal fractional and fractal derivatives. Key properties are derived. Analytical solutions are obtained for linear set-valued Cauchy problems, both without impulses and with impulsive effects, involving this derivative.

Mathematics Subject Classification: 34A08, 34A30, 26E25

Key words and phrases: Impulsive differential equation, set-valued mapping, Hukuhara derivative, conformable fractional derivative, fractal derivative