Nonexistence results for a system of nonlinear fractional integro-differential equations
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., 152, 1–15 (2017)] and Ahmad and Tatar [Turkish J. Math., 43, 2715–2730 (2019)].
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