TY - JOUR T1 - Cauchy problem with $\psi $--Caputo fractional derivative in Banach spaces AU - Benchohra, Mouffak AU - Derbazi, Choukri AU - Baitiche, Zidane PY - 2020 DA - December DO - 10.31197/atnaa.706292 JF - Advances in the Theory of Nonlinear Analysis and its Application JO - ATNAA PB - Erdal KARAPINAR WT - DergiPark SN - 2587-2648 SP - 349 EP - 360 VL - 4 IS - 4 LA - en AB - This paper is devoted to the existence of solutions for certain classes of nonlinear differential equations involving the $\psi $--Caputo fractional derivative in Banach spaces. Our approach is based on a new fixed point theorem with respect to convex-power condensing operator combined with the technique of measures of noncompactness. Finally, two examples are given to illustrate the obtained results. KW - $\psi $--Caputo fractional derivative KW - Cauchy problem KW - convex-power condensing operator KW - fixed point theorem KW - Banach spaces KW - measures of noncompactness CR - x [1] S. Abbas, M. 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