Cauchy problem with $\psi $--Caputo fractional derivative in Banach spaces

Abstract

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.                                                                                                                                                                                                                                                                                                                      

Keywords

• $\psi $--Caputo fractional derivative
• Cauchy problem
• convex-power condensing operator
• fixed point theorem
• Banach spaces
• measures of noncompactness

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