Noninstantaneous impulsive inequalities via conformable fractional calculus

Area of Science:

• Mathematics
• Fractional Calculus
• Inequality Theory

Background:

• Impulsive differential equations and inequalities are crucial in modeling real-world phenomena with sudden changes.
• Fractional calculus offers a powerful framework for describing systems with memory and hereditary properties.
• Conformable fractional calculus provides a more recent and flexible approach to fractional differentiation and integration.

Purpose of the Study:

• To establish new noninstantaneous impulsive inequalities.
• To utilize the conformable fractional calculus framework for deriving these inequalities.
• To contribute to the theoretical development of fractional inequalities.

Main Methods:

• Application of conformable fractional integral and derivative operators.
• Development of techniques for handling noninstantaneous impulses within the fractional calculus context.
• Construction of novel inequality formulations.

Main Results:

• The successful establishment of several new noninstantaneous impulsive inequalities.
• Demonstration of the utility of conformable fractional calculus in this domain.
• The derived inequalities provide new analytical tools.

Conclusions:

• The study successfully established novel noninstantaneous impulsive inequalities using conformable fractional calculus.
• These results expand the toolkit for analyzing fractional differential equations with impulses.
• The findings have potential implications for various fields utilizing fractional calculus.