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

A.  Mugbil

doi:10.37863/umzh.v75i4.6902

A. Mugbil King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia

DOI: https://doi.org/10.37863/umzh.v75i4.6902

Keywords: Nonexistence, global solution, fractional differential equation, Caputo fractional derivative, Riemann--Liouville integral

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., 152, 1–15 (2017)] and Ahmad and Tatar [Turkish J. Math., 43, 2715–2730 (2019)].

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