In this study, the $ (h $-$ \varphi)_R $ and $ (h $-$ \varphi)_M $-contractions with two metrics endowed with a directed graph are examined using auxiliary functions. We propose a set of criteria that guarantees the existence of common fixed points for our contractions. This leads to a generalization of previous results in the literature. Towards our accomplishments, we establish affirmative results that demonstrate solutions to a class of nonlinear two-term fractional differential equations with nonlocal boundary conditions. To further corroborate our major findings, we also provide instances.
Citation: Teeranush Suebcharoen, Watchareepan Atiponrat, Khuanchanok Chaichana. Fixed point theorems via auxiliary functions with applications to two-term fractional differential equations with nonlocal boundary conditions[J]. AIMS Mathematics, 2023, 8(3): 7394-7418. doi: 10.3934/math.2023372
In this study, the $ (h $-$ \varphi)_R $ and $ (h $-$ \varphi)_M $-contractions with two metrics endowed with a directed graph are examined using auxiliary functions. We propose a set of criteria that guarantees the existence of common fixed points for our contractions. This leads to a generalization of previous results in the literature. Towards our accomplishments, we establish affirmative results that demonstrate solutions to a class of nonlinear two-term fractional differential equations with nonlocal boundary conditions. To further corroborate our major findings, we also provide instances.
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Teeranush Suebcharoen, Watchareepan Atiponrat, Khuanchanok Chaichana. Fixed point theorems via auxiliary functions with applications to two-term fractional differential equations with nonlocal boundary conditions[J]. AIMS Mathematics, 2023, 8(3): 7394-7418. doi: 10.3934/math.2023372
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