Some useful inequalities for nabla tempered fractional calculus

TL;DR

This paper develops and analyzes new inequalities for nabla tempered fractional calculus, highlighting its flexibility and potential for practical applications, supported by numerical validation.

Contribution

It introduces and proves novel inequalities for nabla tempered fractional calculus, expanding the mathematical foundation of this flexible calculus.

Findings

New inequalities for nabla tempered fractional calculus are established.

Numerical results confirm the validity and potential of the developed properties.

Tempered functions enhance the applicability and effectiveness of fractional calculus.

Abstract

This paper gives particular emphasis to the nabla tempered fractional calculus, which involves the multiplication of the rising function kernel with tempered functions, and provides a more flexible alternative with considerable promise for practical applications. Some remarkable inequalities for such nabla fractional calculus are developed and analyzed, which greatly enrich the mathematical theory of nabla tempered fractional calculus. Numerical results confirm the validity of the developed properties once again, which also reveals that the introduction of tempered function provides high value and huge potential.