Mohammed D. Kassim, Khaled M. Furati, Nasser-eddine Tatar
Abstract:
We study the boundedness and asymptotic behavior of solutions for a
class of nonlinear fractional differential equations. These equations
involve two Riemann-Liouville fractional derivatives of different orders.
We determine fairly large classes of nonlinearities and appropriate underlying
spaces where solutions are bounded, exist globally and decay to zero as a
power type function. Our results are obtained by using generalized versions
of Gronwall-Bellman inequality, appropriate regularization techniques and
several properties of fractional derivatives. Three examples are given to
illustrate our results.
Submitted July 7, 2016. Published October 31, 2016.
Math Subject Classifications: 34C11, 42B20, 34E10.
Key Words: Regularization technique; Mittag-Leffler function; power type decay;
weighted space.
Show me the PDF file (245 KB), TEX file for this article.
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Mohammed D. Kassim King Fahd University of Petroleum and Minerals Department of Mathematics and Statistics Dhahran 31261, Saudi Arabia email: dahan@kfupm.edu.sa |
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Khaled M. Furati King Fahd University of Petroleum and Minerals Department of Mathematics and Statistics Dhahran 31261, Saudi Arabia email: kmfurati@kfupm.edu.sa |
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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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