A solution of the fractional differential equations in the setting of $b$-metric space - Afshari, H.; Karapinar, E. (Carpathian Mathematical Publications, 2021)
In this paper, we study the existence of solutions for the following differential equations by using a fixed point theorems \[ \begin{cases} D^{\mu}_{c}w(\varsigma)\pm D^{ u}_{c}w(\varsigma)=h(\varsigma,w(\varsigma)),& \varsigma\in J,\ \ 0< u<\mu<1,\\ w(0)=w_0,& \ \end{cases} \] where $D^{\mu}$, $D^{ u}$ is the Caputo derivative of order $\mu$, $ u$, respectively and $h:J\times \mathbb{R}\rightarrow \mathbb{R}$ is continuous. The results are well demonstrated with the aid of exciting examples.