Alireza Khalili Golmankhaneh, Carlo Cattani, Diana T. Pham, Mahmoud Abdel-Aty, Fractal integral equations, Vol. 2024 (2024), Article ID 22, pp. 1-14

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DOI: 10.23952/jnfa.2024.22

Received 11 September, 2024; Accepted September 26, 2024; Published October 16, 2024

 

Abstract. In this paper, we introduce fractal volterra integral equations and fractal Fredholm integral equations. We derive the corresponding fractal differential equations and provide solutions to several examples. As an application, we solve the fractal linear oscillator equation and plot its solution to illustrate the impact of fractal support on the results. This work extends classical integral and differential equation theories into the fractal domain, highlighting the unique behaviors and solutions that emerge from fractal structures.

 

How to Cite this Article:
A.K. Golmankhaneh, C. Cattani, D.T. Pham, M. Abdel-Aty, Fractal integral equations, J. Nonlinear Funct. Anal. 2024 (2024) 22.