SOLVING FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS IN HEAT CONDUCTION AND BIOLOGICAL MODELING
DOI:
https://doi.org/10.55640/Keywords:
fractional integro-differential equations, Neumann series, Caputo derivative, convergence, heat conduction, biological modeling.Abstract
This article analyzes the method of solving fractional integro-differential equations using the Neumann series. The convergence of the solution for equations based on the Caputo fractional derivative is proven by applying the Banach fixed-point theorem. The efficiency of the method is demonstrated through numerical examples and is applied to problems of heat conduction and biological population dynamics. The results are of significant importance in modern materials science and biology, and contribute to the advancement of fractional mathematics within the scientific community of Uzbekistan.
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