Abstract
In this article, we deal with a fully fractional thermostat model in the settings of the RiemannâLiouville fractional derivatives. The equivalences between the fractional differential equations and the corresponding VolterraâFredholm integral equations are rigorously derived. By choosing an appropriate weighted Banach space of continuous functions, we employ two standard fixed-point theorems, LerayâSchauder alternative and Banach contraction principle, to establish the existence of blow-up solutions â the unbounded mathematical solutions in the operational interval. Furthermore, an implicit numerical scheme based on the right product rectangle rule is presented, which provides the numerical approximation of the obtained solution. Some examples are provided to validate our theoretical findings, along with numerical simulations of the solutions.
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More From: Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena
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