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This paper considers a coupled hybrid thermostat system driven by the Ã-Caputo fractional derivative in a Banach algebra. We employ a version of Darbo’s fixed-point theorem combined with the measure of noncompactness (MNC) technique to establish certain existence results. Additionally, an example is provided to illustrate our findings. [ABSTRACT FROM AUTHOR]

A study of a class of nonlinear differential equations involving the φ -Caputo type derivative in a Banach space framework is presented. Weissinger's and Meir-Keeler's fixed-point theorems are used to achieve some quantitative results. Two illustrative examples are provided to justify the theoretical results. A study of a class of nonlinear differential equations involving the -Caputo type derivative in a Banach space framework is presented. Weissinger's and Meir-Keeler's fixed-point theorems are used to achieve some quantitative results. Two illustrative examples are provided to justify the theoretical results. [ABSTRACT FROM AUTHOR]