A solution of the fractional differential equations in the setting of $b$-metric space




complete $b$-metric space, Caputo derivative, $\alpha$-$\psi$-Geraghty contractive type mapping
Published online: 2021-12-29


In this paper, we study the existence of solutions for the following differential equations by using a fixed point theorems \[ \begin{cases} D^{\mu}_{c}w(\varsigma)\pm D^{\nu}_{c}w(\varsigma)=h(\varsigma,w(\varsigma)),& \varsigma\in J,\ \ 0<\nu<\mu<1,\\ w(0)=w_0,& \ \end{cases} \] where $D^{\mu}$, $D^{\nu}$ is the Caputo derivative of order $\mu$, $\nu$, respectively and $h:J\times \mathbb{R}\rightarrow \mathbb{R}$ is continuous. The results are well demonstrated with the aid of exciting examples.

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How to Cite
Afshari, H.; Karapinar, E. A Solution of the Fractional Differential Equations in the Setting of $b$-Metric Space. Carpathian Math. Publ. 2021, 13, 764-774.