Abstract
In this article, we consider some classes of nonlinear fractional differential equations
with singularity take the form
b‘u(t,
where / C J :— [0,1] and z U : — (z C :| z |< 1 ) . Our purpose is to establish a result similar
to the k-summabi1ity known in the case of singular ordinary differential equations. It's shown that
under some conditions, all formal solutions are Borel summable or k-summable with respect to z C U
in all
directions except at most a countable number.
Keywords: Fractional calculus; Fractional differential equation; Holomorphic solution; Unit disk;
Riemann-Liouville operators; Nonlinear; Singular fractional differential equation; Borel summable.
AMS Mathematics Subject Classification: 30C25
