On Approximation Properties of Fractional Integral for A-Fractal Function

T. M. C. Priyanka, R. Valarmathi, Kishore Bingi, A. Gowrisankar and Waleed Adel

Mathematical Problems in Engineering, 2022, vol. 2022, 1-17

Abstract: In this paper, the Riemann–Liouville fractional integral of an A-fractal function is explored by taking its vertical scaling factors in the block matrix as continuous functions from 0,1 to ℠. As the scaling factors play a significant role in the generation of fractal functions, the necessary condition for the scaling factors in the block matrix is outlined for the newly obtained function. The resultant function of the fractional integral is demonstrated as an A-fractal function if the scaling factors obey the necessary conditions. Furthermore, this article proposes a fractional operator which defines the Riemann–Liouville fractional integral of an A-fractal function for each continuous function on CI,℠2, where CI,℠2 is the space of all continuous functions from closed interval I⊂℠to ℠2. In addition, the approximation properties such as linearity, boundedness, and semigroup property of the proposed fractional operator are investigated.

Date: 2022
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/mpe/2022/6409656.pdf (application/pdf)
http://downloads.hindawi.com/journals/mpe/2022/6409656.xml (application/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:6409656

DOI: 10.1155/2022/6409656

Access Statistics for this article

More articles in Mathematical Problems in Engineering from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().