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This paper is devoted to the existence of solutions for certain classes of nonlinear differential equations involving the Caputo - Hadamard fractional-order with $\mathrm{p}$ - Laplacian operator in Banach spaces. The arguments are based on M \" {o} nch's fixed point theorem combined with the technique of measures of noncompactness . An example is also presented to illustrate the effectiveness of the main results.

SOLVABILITY FOR A CLASS OF NONLINEAR CAPUTO-HADAMARD FRACTIONAL DIFFERENTIAL EQUATIONS WITH p-LAPLACIAN OPERATOR IN BANACH SPACES