The generalized nonlocal fractal calculus: An efficient tool for fractal circuit analysis

Abstract

Purpose
The purpose of this paper is to propose a novel nonlocal fractal calculus scheme dedicated to the analysis of fractal electrical circuit, namely, the generalized nonlocal fractal calculus.

Design/methodology/approach
For being generalized, an arbitrary kernel function has been adopted. The condition on order has been derived so that it is not related to the γ-dimension of the fractal set. The fractal Laplace transforms of our operators have been derived.

Findings
Unlike the traditional power law kernel-based nonlocal fractal calculus operators, ours are generalized, consistent with the local fractal derivative and use higher degree of freedom. As intended, the proposed nonlocal fractal calculus is applicable to any kind of fractal electrical circuit. Thus, it has been found to be a more efficient tool for the fractal electrical circuit analysis than any previous fractal set dedicated calculus scheme.

Originality/value
A fractal calculus scheme that is more efficient for the fractal electrical circuit analysis than any previous ones has been proposed in this work.

Keywords: Caputo sense, Fractal set, Fractal electrical circuit, Interpolated sense, Kernel, Nonlocal fractal calculus, Riemann–Liouville sense

รศ. ดร.รวิศวร์ บานชื่น – Assoc. Prof. Dr. Rawid Banchuin. 2568 (2025). The generalized nonlocal fractal calculus: an efficient tool for fractal circuit analysis Available to Purchase. บทความ (Paper). ปริญญาโท (Master’s Degree). บัณฑิตวิทยาลัย (Graduate School). วิทยาศาสตรมหาบัณฑิต สาขาวิชาเทคโนโลยีสารสนเทศ – Master of Science Program in Information Technology. วท.ม. (เทคโนโลยีสารสนเทศ) – M.Sc. (Information Technology). Bangkok: Siam University