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Keywords
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(k,\Phi)–Hilfer fractional derivative, existence, nonlinear analysis, Ulam stability, generalized Banach spaces, Lipschitzian matrix
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Abstract
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In this paper, we study a coupled fully hybrid system of (k,\Phi)–Hilfer fractional differential
equations equipped with non-symmetric (k,\Phi)–Riemann-Liouville (RL) 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 (GBS). Moreover, the Ulam–
Hyers (UH) 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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