| Summary: | In this paper, we study a coupled fully hybrid system of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi mathvariant="bold">k</mi><mo>,</mo><mi mathvariant="sans-serif">Φ</mi><mo>)</mo></mrow></semantics></math></inline-formula>–Hilfer fractional differential equations equipped with non-symmetric <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi mathvariant="bold">k</mi><mo>,</mo><mi mathvariant="sans-serif">Φ</mi><mo>)</mo></mrow></semantics></math></inline-formula>–Riemann-Liouville (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">RL</mi></semantics></math></inline-formula>) integral conditions. To prove the existence and uniqueness results, we use the Krasnoselskii and Perov fixed-point theorems with Lipschitzian matrix in the context of a generalized Banach space (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">GBS</mi></semantics></math></inline-formula>). Moreover, the Ulam–Hyers (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">UH</mi></semantics></math></inline-formula>) stability of the solutions is discussed by using the Urs’s method. Finally, an illustrated example is given to confirm the validity of our results.
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