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A fixed point approach to the solution of singular fractional differential equations with integral boundary conditions

2021
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Advances in Difference Equations
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AbstractIn 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 α: $$ \begin{aligned} &{}^{c}D^{\alpha }v(t) + h \bigl(t,v(t) \bigr) = 0,\quad 0< t< 1, \\ &v"(0) = v"'(0) = 0, \\ &v'(0) = v(1) = \beta \int _{0}^{1} v(s) \,ds, \end{aligned} $$ D α c v ( t ) + h ( t , v ( t )

doi:10.1186/s13662-021-03225-y
fatcat:mywfnipqz5g65eo3xlrr7nsnza