A Coupled Singular Fractional Integro-Differential System with Bessel Operator: Existence, Uniqueness, and Stability
- 1Mathematics Department, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
Abstract
This paper investigates a coupled system of two-dimensional singular fractional partial differential equations within a bounded domain. The system is defined by Neumann boundary conditions, non-local weighted integral constraints, memory terms, Caputo fractional derivatives, and a Bessel operator. Physically, the model captures memory effects, linear dissipation, and thermoelastic coupling to describe anomalous diffusion-wave dynamics and fractional viscoelastic thermoelasticity in cylindrically symmetric media. By developing a functional framework based on weighted Sobolev spaces and utilizing energy methods with integro-differential operators, we obtain essential a priori estimates. These estimates ensure that the solutions are unique and continuously dependent on the data. Furthermore, we establish the existence of solutions by demonstrating that the associated operator has a dense range and a trivial orthogonal complement. Ultimately, this study makes a substantial contribution to the well-posedness theory of singular fractional thermoelastic models subject to nonlocal conditions.
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BibTeX
@article{mesloub2026coupled,
title = {{A Coupled Singular Fractional Integro-Differential System with Bessel Operator: Existence, Uniqueness, and Stability}},
author = {Said Mesloub and Rowaida Alrajhi},
journal = {Mathematics},
year = {2026},
month = oct,
doi = {10.3390/math14203662},
url = {https://www.mdpi.com/2227-7390/14/20/3662},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - A Coupled Singular Fractional Integro-Differential System with Bessel Operator: Existence, Uniqueness, and Stability
AU - Said Mesloub
AU - Rowaida Alrajhi
PY - 2026
DA - 2026/10/09
JO - Mathematics
DO - 10.3390/math14203662
UR - https://www.mdpi.com/2227-7390/14/20/3662
AB - This paper investigates a coupled system of two-dimensional singular fractional partial differential equations within a bounded domain. The system is defined by Neumann boundary conditions, non-local weighted integral constraints, memory terms, Caputo fractional derivatives, and a Bessel operator. Physically, the model captures memory effects, linear dissipation, and thermoelastic coupling to describe anomalous diffusion-wave dynamics and fractional viscoelastic thermoelasticity in cylindrically symmetric media. By developing a functional framework based on weighted Sobolev spaces and utilizing energy methods with integro-differential operators, we obtain essential a priori estimates. These estimates ensure that the solutions are unique and continuously dependent on the data. Furthermore, we establish the existence of solutions by demonstrating that the associated operator has a dense range and a trivial orthogonal complement. Ultimately, this study makes a substantial contribution to the well-posedness theory of singular fractional thermoelastic models subject to nonlocal conditions.
SN - 2227-7390
ER -