Abstract

Abstract In this paper, we prove the existence and uniqueness of Caputo time fractional pseudo-hyperbolic equations of higher order with purely nonlocal conditions of integral type. We use an a priori estimate method; the so-called energy inequalities method, based on some functional analysis tools, is developed for a Caputo time fractional of 2 ⁢ m {2m} -th and ( 2 ⁢ m + 1 ) {(2m+1)} -th order and the density of the range of the operator generated by the considered problem. Using the Laplace transform and homotopy perturbation, we find a semi-analytical solution. Finally, we give some examples for illustration.

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