Nonexistence results for a system of nonlinear fractional integro-differential equations

Abstract

UDC 517.9 We investigate the nonexistence of (nontrivial) global solutions for a system of nonlinear fractional equations.  Each equation involves n fractional derivatives, a subfirst-order ordinary derivative, and a nonlinear source term.  The fractional derivatives are of the Caputo type of order between 0 and 1.   The nonlinear sources have the form of the convolution of a function of  state with (possibly singular) kernel.  We generalize the results available in the literature, in particular, the results obtained by Mennouni and Youkana [Electron. J. Different. Equat., <strong>152</strong>, 1–15 (2017)] and Ahmad and Tatar [Turkish J. Math., <strong>43</strong>, 2715–2730 (2019)].