The Combined Effects of Hyers-Ulam Stability and Riemann-Liouville Fractional Derivatives on Symmetric and Asymmetric Boundary Conditions,"Thermal Explosion with Arrhenius Kinetics inParallel Plates"
DOI:
https://doi.org/10.62054/ijdm/0302.11iAbstract
This article investigates the combination of Hyers-Ulam stability and Riemann-Liouville fractional derivatives in thermal explosion phenomena with Arrhenius kinetics between two parallel plates with both symmetric and asymmetric boundary conditions. The fractional order of the equation presented here is a generalization of the classical heat conduction equation with memory effects. We detail the formulation of Riemann-Liouville fractional operators, and we prove existence, uniqueness, and Hyers-Ulam stability, as well as derive the critical Frank-Kamenetskii parameters for thermal ignition. We also include a comparison of analytical results with numerical simulations. For the asymmetry case, we demonstrate a decrease in the value of the critical parameter, and for $\theta_w=0$, we derive the symmetric results. The theory is supported by graphs and data tables.
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Copyright (c) 2026 Adenegan K. Emmanuel (Author)
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