### The nonlinear time-fractional differential equations with integral conditions

JPRM-Vol. 17 (2021), Issue 2, pp. 168 – 181 Open Access Full-Text PDF

**H. Merad, F. Merghadi, A. Merad**

**Abstract:**In this paper, we present a nonlinear equation modeling a time-fractional pseudoparabolic problem, involving fractional Caputo derivative where the fractional order is 0 < α < 1. We first started with the associated linear problem, we establish the energy inequalities to obtaine a priori estimate,and demonstrate the density of the operator’s range generated. Accordingly, the existence and uniqueness of the weak solutions are given, then we use the preceding results to handle the nonlinear case via an iterative process.