2023/02/08 by Yiheng Wei, Wei, Yiheng, Linlin Zhao +5
Mathematics · #FOS: Mathematics #Fractional Differential Equations Solutions #General Mathematics (math.GM) #Mathematical functions and polynomials #Nonlinear Differential Equations Analysis
paper · pdf · doi:10.48550/arxiv.2302.04674
openalex publication_date 2023/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Despite many applications regarding fractional calculus have been reported in literature, it is still unknown how to model some practical process. One major challenge in solving such a problem is that, the nonlocal property is needed while the infinite memory is undesired. Under this context, a new kind nabla fractional calculus accompanied by a tempered function is formulated. However, many properties of such fractional calculus needed to be discovered. From this, this paper gives particular emphasis to the topic. Some remarkable properties like the equivalence relation, the nabla Taylor formula, and the nabla Laplace transform for such nabla fractional calculus are developed and analyzed. It is believed that this work greatly enriches the mathematical theory of nabla tempered fractional calculus and provides high value and huge potential for further applications.