In this article, we give sufficient conditions for the existence of solutions for a new coupled system of second-order implicit differential equations with Hadamard and Erdelyi-Kober fractional integral boundary conditions and nonlocal conditions at the boundaries in Banach space. The main result is based on a Mönch fixed point theorem combined with the measure of noncompactness of Kuratowski; an example is given to illustrate our approach.
Hadamard fractional derivative, Erdelyi--Kober fractional integral, Caputo fractional derivative, measure of noncompactness of Kuratowski, Mönch fixed point theorem, coupled system of differential equations
BERRABAH, FATIMA ZOHRA; HEDIA, BENAOUDA; and HENDERSON, JOHNNY
"A fully Hadamard and Erdelyi-Kober-type integral boundary value problem of acoupled system of implicit differential equations,"
Turkish Journal of Mathematics: Vol. 43:
3, Article 18.
Available at: https://journals.tubitak.gov.tr/math/vol43/iss3/18