Solving Fractional Differential Equations in b-metric Spaces Tailored with a Directed Graph
DOI:
https://doi.org/10.29020/nybg.ejpam.v18i4.6811Keywords:
\textit{$\mathfrak{b}$-metric space ($\mathfrak{b}$MS), Fractional differential equation, auxiliary function, directed graph ($\mathcal{DG}$), coincidence point($\mathcal{CP}$), Caputo Fractional Differential Equation ($\mathcal{CFDE}$).}Abstract
This study introduces an extended class of contractions incorporating auxiliary functions. We examine the existence of solutions for Caputo fractional differential equations with integral boundary conditions within the framework of b-metric spaces endowed with a directed graph. The established findings not only generalize but also unify a number of significant results in the existing literature, as demonstrated by supporting theoretical developments and illustrative examples.
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Copyright (c) 2025 Dur-e-Shehwar Sagheer, Haitham Qawaqneh, Samina Batul, Ismat Urooj, Zainab Rahman, Hassen Aydi
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