arXiv subjects

Taylan Demir

Publications and source records attributed to Taylan Demir.

7 recordsLinked to original sources

arXiv2026

State dependent delay differential equations with distributed memory

We investigate state dependent delay differential equations with distributed memory, combining discrete state dependent delays and a convolution type memory operator. Under Lipschitz type assumptions on the delay, kernel, and nonlinear term, we establish local well posedness using a fixed point argument in a Banach space of histories. The distributed memory operator is shown to be locally Lipschitz, ensuring existence and uniqueness. As a benchmark, we analyze a logistic model with a Gamma distributed memory kernel of order two. The convolution term is reduced to a finite dimensional form, yielding an explicit characteristic equation and closed form Hopf bifurcation threshold and frequency. The results show that higher order memory kernels may induce oscillatory dynamics, unlike purely exponential memory, and provide a rigorous framework for stability and bifurcation analysis in delay systems with state dependent memory.

math.DS↗

arXiv2025

Painlev\'e Integrability And Shifted Nonlocal Reductions Of A Variable Coefficient Coupled HI Mkdv System

We analyze a variable coefficient coupled HI mKdV system that has shifted nonlocal reductions. The Weiss Tabor Carnevale test gives us coefficient restrictions to perform a time reparametrization to achieve an autonomous integrable model. We also show a Hirota bilinear form along with a simplified example to demonstrate how the shifted symmetries create new symmetry centers, but do not affect the shape of the soliton.

nlin.SI↗

arXiv2025

fractional-time deformation of quantum coherence in open systems: a non-markovian framework beyond lindblad dynamics

In this paper, we propose a fractional time extension of the Quan tum Master Equation. We introduce a Caputo-type fractional derivative in time as an extension of the exponential decay of the Lindblad framework through the incorporation of fractional derivatives into the Lindblad framework. We show that the analytical and numerical results of our analytical and numerical models, demonstrate that fractional dynamics produces long-memory coherence decay naturally and provides an interpretable and flexible model of non-Markovianity.

quant-ph↗

arXiv2025

Real Time Magnetic Field Line Tracing In The Magnetosphere Via Adaptive Error Bounded Integration

Field line tracing is one of the fundamental computational tools used in the study of the magnetosphere, which helps in many areas including footprint mapping, connectivity analysis and real-time visualisation. This note describes an implementation approach to error-bounded adaptive integration of the field line differential equation (ODE), where an embedded Runge-Kutta pair is used in conjunction with event detection, allowing robust localisation of footprint locations on spacecraft. The method is validated against an analytic dipole field model as well as an international geomagnetic reference field (IGRF)-based geomagnetic configuration.

physics.geo-ph↗

arXiv2025

Adaptive Wavelet-Galerkin Modelling of Heat Conduction in Heterogeneous Composite Materials

We present an adaptive wavelet Galerkin method for transient heat conduction in heterogeneous composite materials. The approach combines multiresolution wavelet bases with an implicit time discretization to efficiently resolve sharp temperature gradients near material interfaces and boundary layers. Adaptive refinement is driven by wavelet coefficients, significantly reducing the number of degrees of freedom compared to uniform discretizations. Numerical examples demonstrate accurate resolution of layered, inclusion-based, and functionally graded composites with improved computational efficiency.

math.NA↗

arXiv2025

Seismic wave propagation in viscoelastic media under Atangana-Baleanu fractional dynamics: Model formulation and numerical simulations

We propose a one-dimensional viscoelastic seismic-wave model driven by the Atangana-BaleanuCaputo fractional derivative with a non-singular Mittag-Leffler kernel. A finite-difference discretization in space and an Adams-Bashforth-Moulton predictor-corrector scheme in time are used to compute solutions for several fractional orders. Simulations indicate that fractional memory alters both attenuation and dispersion, leading to non-exponential energy decay compared with the classical integer-order case.

physics.geo-ph↗

arXiv2025

Atangana-Baleanu Regularized Wavelet Compression For Astronomical Time-Series

Astronomical light curves are noisy and irregular, so compression must reduce size without erasing weak transients. We propose a fractional wavelet compression method where wavelet coefficients are regularized via an Atangana Baleanu Caputo derivative with a nonsingular Mittag Leffler kernel. The induced long memory smoothing suppresses noise while preserving coherent transits, flares and oscillations. We give the coefficient level formulation, an efficient implementation, and comparisons with classical discrete wavelet thresholding, showing competitive compression with improved retention of low-amplitude events.

astro-ph.IM↗