Browsing by Author "Valdes, Juan E. Napoles"

Now showing 1 - 3 of 3

Fractal Rosenau-Burgers Equation
(Springer Int Publ Ag, 2025) Golmankhaneh, Alireza Khalili; Karaagac, Berat; Jorgensen, Palle E. T.; Valdes, Juan E. Napoles
This paper begins with a concise summary of fractal calculus, laying out the foundational concepts necessary for further analysis. We then introduce the fractal Rosenau-Burgers equation and present its analytical solution. Perturbation methods for solving this nonlinear fractal differential equation are developed and examined in detail. Building upon this framework, we investigate practical applications such as signal propagation in fractal transmission lines and transport phenomena in porous and fractal media. Additionally, we provide graphical illustrations of the solutions to demonstrate the effects of fractal spatial and temporal dimensions on these models.
Fuzzy Stability in the Sense of Hyers-Ulam of a Functional Equation on Quadratic Forms
(Taru Publications, 2023) Farahani, Moahmmad Reza; Valdes, Juan E. Napoles; Cancan, Murat; Jafari, Saeid
We obtain a general solution of the 2-variable quadratic functional equation zeta(y(1) + y(2), y(3) + y(4)) + zeta(y(1)-y(2), y(3)-y(4)) = 2 zeta(y(1), y(3)) + 2 zeta(y(2), y(4)) and discuss the stability of the above functional equation, while the quadratic form zeta(a, b) = alpha a(2) + beta ab + gamma c(2) is a solution of our functional equation.
On Initial Value Problems of Fractal Delay Equations
(Elsevier Science inc, 2023) Golmankhaneh, Alireza Khalili; Tejado, Ines; Sevli, Hamdullah; Valdes, Juan E. Napoles
In this paper, we give a brief summary of fractal calculus. Fractal functional differential equations are formulated as a framework that provides a mathematical model for the phe-nomena with fractal time and fractal structure. Fractal retarded, neutral, and renewal delay differential equations with constant coefficients are solved by the method of steps and us-ing Laplace transform. The graphs of solutions are given to show the details.(c) 2023 Elsevier Inc. All rights reserved.