Electron. J. Differential Equations, Vol. 2017 (2017), No. 134, pp. 1-16.

Asymptotic power type behavior of solutions to a nonlinear fractional integro-differential equation

Ahmad M. Ahmad, Khaled M. Furati, Nasser-Eddine Tatar

Abstract:
This article concerns a general fractional differential equation of order between 1 and 2. We consider the cases where the nonlinear term contains or does not contain other (lower order) fractional derivatives (of Riemann-Liouville type). Moreover, the nonlinearity involves also a nonlinear non-local in time term. The case where this non-local term has a singular kernel is treated as well. It is proved, in all these situations, that solutions approach power type functions at infinity.

Submitted April 27, 2017. Published May 17, 2017
Math Subject Classifications: 35B40, 34A08, 26D10.
Key Words: Asymptotic behavior; fractional integro-differential equation; Riemann-Liouville fractional derivative; nonlocal source; integral inequalities.

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Ahmad M. Ahmad
King Fahd University of Petroleum and Minerals
Department of Mathematics and Statistics
Dhahran 31261, Saudi Arabia
email: mugbil@kfupm.edu.sa
Khaled M. Furati
King Fahd University of Petroleum and Minerals
Department of Mathematics and Statistics
Dhahran 31261, Saudi Arabia
email: kmfurati@kfupm.edu.sa
Nasser-Eddine Tatar
King Fahd University of Petroleum and Minerals
Department of Mathematics and Statistics
Dhahran 31261, Saudi Arabia
email: tatarn@kfupm.edu.sa

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