Fractional differential and integral operations and cumulative processes

2016/08/26 by Fevzi Büyükkılıç, Buyukkilic, Fevzi, Z. Ok Bayrakdar +3
Mathematics · #FOS: Physical sciences #Fractional Differential Equations Solutions #Iterative Methods for Nonlinear Equations #Mathematical Physics (math-ph) #Mathematical functions and polynomials #Statistical Mechanics (cond-mat.stat-mech)

paper · pdf · doi:10.48550/arxiv.1608.08534

openalex publication_date 2016/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this study the general formula for differential and integral operations of fractional calculus via fractal operators by the method of cumulative diminution and cumulative growth is obtained. The under lying mechanism in the success of traditional fractional calculus for describing complex systems is uncovered. The connection between complex physics with fractional differentiation and integration operations is established.

Citations

• The Fractal Geometry of Nature
• Fractional Differential Equations

Related

• Studies of fractal structures and processes using methods of fractional\n calculus
• About Fractional Calculus and its Applications in Physics
• Definition of fractal measures arising from fractional calculus
• On Fractals and Fractional Calculus Motivated by Complex Systems
• Fractional Differential Equations