Abstract
One of best ways for increasing our abilities in exact modeling of natural phenomena is working with a singular version of different fractional differential equations. As is well known, multi-singular equations are a modern version of singular equations. In this paper, we investigate the existence of solutions for a multi-singular fractional differential system. We consider some particular boundary value conditions on the system. By using the α-ψ-contractions and locating some control conditions, we prove that the system via infinite singular points has solutions. Finally, we provide an example to illustrate our main result.
Highlights
The fractional derivatives have an long history
Much work is conducted in the field of fractional differential equations among which some have a singular point to control these sorts of points ([16,17,18,19]) and we have nonlinear delay-fractional differential equations ([20,21,22,23])
2014 Jleli et al proved the existence of a positive solution for the singular fractional boundary value problem Dαu(t) + f (t, u(t)) = 0 with u(0) = u (0) = 0 and u (1) =
Summary
It is natural that many phenomena could be modeled by using singular fractional integro-differential equations. In 2011, Feng et al studied the existence of a solution for the singular system 2014 Jleli et al proved the existence of a positive solution for the singular fractional boundary value problem Dαu(t) + f (t, u(t)) = 0 with u(0) = u (0) = 0 and u (1) =
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