University of Guilan Journal of Mathematical Modeling 2345-394X 9 3 2021 09 01 Mixed fractional differential equation with nonlocal conditions in Banach spaces 451 463 4609 10.22124/jmm.2021.18439.1582 EN Abdellatif Boutiara Laboratory of Mathematics And Applied Sciences University of Ghardaia, 47000. Algeria Journal Article 2020 12 19 This paper is devoted to study the existence of solution for a class of  nonlinear differential equations with nonlocal boundary conditions involving the right Caputo and left Riemann--Liouville fractional derivatives. Our approach is based on Darbo's fixed point theorem associated with the Hausdorff measure of noncompactness. The obtained results generalize and extend some of the results found in the literature. Besides, the reported results concerned in the Banach space's sense. In the end,  an example illustrates our acquired results. Right Caputo and left Riemann--Liouville fractional derivatives nonlocal boundary conditions existence Banach spaces Darbo's fixed point theorem Hausdorff measure of noncompactness https://jmm.guilan.ac.ir/article_4609_d62226793e9621e109382e4761d71a46.pdf