Special Session 108: New Trends in Fractional Modelling with General Kernel

New aspects of the generalized operators

DUMITRU BALEANU Lebanese American University,Beirut,Lebanon Lebanon Co-Author(s):

Abstract: The fractional calculus is an extension of meaning and it is an important field of the applied mathematics. In my talk I will review the concept of the generalized fractional operators and their applications. Illustrative examples will be given.

Generalization of 1D-Asymmetric Harmonic Oscillator Model via Different Kernels

Ozlem Defterli Associate Professor Dr., Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, Ankara Turkey Co-Author(s):    Dumitru Baleanu,Amin Jajarmi, Ozlem Defterli, Noorhan Alshaikh, Jihad Asad

Abstract: The fractional dynamics of a one-dimensional asymmetric harmonic oscillator model having quadratic nonlinearity is investigated within a generalized kernel. Using the principles of the calculus of variations, a system of two-coupled fractional differential equations with a nonlinear component is derived as fractional Euler-Lagrange equations of the corresponding system. The numerical solution to the system is evaluated and then simulated concerning various model parameter values, including mass, linear and quadratic nonlinear stiffness, and the order of the fractional derivative.

Coupled Dynamics Of Caputo Memory Effects And Time Delays In Fractional Physical Models

Imad A Jaradat Abdullah Al-Salem University Kuwait Co-Author(s):    NA

Abstract: This work explores the impact of spatiotemporal memory effects, governed by Caputo derivatives, and proportional time delays on the dynamics of fractional physical models. Using a novel transformation method, these models are reformulated into recurrence relations that result in the derivation of convergent series solutions of the Cauchy product type. The results demonstrate that these parameters significantly influence the system`s evolution over time and show a continuous transition from stationary to dynamic states, with the Caputo derivative orders functioning as homotopy parameters in a topological context. Additionally, a detailed graphical analysis highlights the parallel roles of time delays and fractional temporal derivatives, further supporting the view of Caputo derivatives as indicators of memory effects.

The treatment of conformable electromagnetic theory of Maxwell as a singular system

Eqab M. Rabei Al al-Bayt university Jordan Co-Author(s):    Mohamed Ghaleb Al-Masaeed and Dumitru Baleanu

Abstract: documentclass{article} \usepackage{graphicx} % Required for inserting images \title{The treatment of conformable electromagnetic theory of Maxwell as a singular system } \author{Eqab.M.Rabei$^{1,2}$, Mohamed Ghaleb Al-Masaeed $^{3,4}$, Dumitru Baleanu$^{5}$ \$^1$Science Department, Faculty of Science, Jerash Private University\ $^2$Physics Department, Faculty of Science, Al al-Bayt University,\ P.O. Box 130040, Mafraq 25113, Jordan\$^3$Ministry of Education, Jordan\ $^4$Ministry of Education and Higher Education, Qatar\$^5$Department of Mathematics, Cankaya University, Ankara, Turkey\eqabrabei@gmail.com\moh.almssaeed@gmail.com} \begin{document} \maketitle \begin{abstract} The study explores the conformable electromagnetic field theory. The concept of the conformable delta function is introduced. Subsequently, the conformable Maxwell`s equations are derived. \ \textit{Keywords:}conformable derivative; Singular systems; constrained system; Dirac theory ; Lagrangian formulations; Hamiltonian formulations. \end{abstract} \end{document}