Abstract
In this article, we first demonstrate a fixed point result under certain contraction in the setting of controlled b-Branciari metric type spaces. Thereafter, we specifically consider a following boundary value problem (BVP) for a singular fractional differential equation of order : where , , is the Caputo fractional derivative and may be singular at .<disp-formula id="Equa"><mml:mtable columnalign="right left" columnspacing="0.2em">Dalpha cv(t)+h(t,v(t))=0,<mml:mspace width="1em"></mml:mspace>0<t<1,v '' (0)=v'"(0)=0,v ' (0)=v(1)=beta integral 01v(s)<mml:mspace width="0.2em"></mml:mspace>ds,</mml:mtable><graphic position="anchor" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13662_2021_3225_Article_Equa.gif"> </disp-formula>alpha hEventually, we investigate the existence and uniqueness of solutions of the aforementioned boundary value problem of order via a fixed point problem of an integral operator.