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February 9, 2026Open Access

On the quantitative weighted generalization of Jafari transform

Key Points

The aim is to propose a new quantitative weighted transform based on the Jafari transform and explore its mathematical foundations.
Reviewed the mathematical tools related to the Jafari transform.
Introduced the quantitative weighted Jafari transform and ensured its existence via a theorem.
Derived transforms for fractional derivatives and integrals with weights h and w.
Applied theoretical findings to solve classical and fractional initial value problems.
Established existence and fundamental properties of the new transform.
Successfully derived fractional derivatives and integrals relevant to the weighted transform.
Applied findings effectively to classical initial value problems with observable enhancements.

Abstract

In this paper, a quantitative weighted transform based on the Jafari transform is proposed, and the mathematical foundations of this new transform are investigated. In the first section, some information about Jafari transform and some mathematical tools are reviewed. In the second section, the quantitative weighted Jafari transform is introduced, its existence guaranteed through a theorem, and its fundamental properties are examined. Additionally, transforms of the fractional derivative and fractional integral of a function with respect to a function h and a w-weight are obtained. In the third section, the theoretical findings are applied to solve classical and fractional initial value problems based on a function h and w-weight. In the last section, the results are discussed.

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