TY - JOUR
T1 - Fractional integral inequalities and applications
AU - Denton, Zachary
AU - Vatsala, A. S.
PY - 2010/2/1
Y1 - 2010/2/1
N2 - Fractional integral inequality results when 0 < q < 1 are developed when the nonlinear term is increasing in u and satisfies a one sided Lipschitz condition. Using the integral inequality result and the computation of the solution of the linear fractional equation of variable coefficients, Gronwall inequality results are established. This yields the results of q = 1 as a special case. As an application of this, the uniqueness and continuous dependence of the solution on the initial parameters of the nonlinear fractional differential equations are established. © 2009 Elsevier Ltd. All rights reserved.
AB - Fractional integral inequality results when 0 < q < 1 are developed when the nonlinear term is increasing in u and satisfies a one sided Lipschitz condition. Using the integral inequality result and the computation of the solution of the linear fractional equation of variable coefficients, Gronwall inequality results are established. This yields the results of q = 1 as a special case. As an application of this, the uniqueness and continuous dependence of the solution on the initial parameters of the nonlinear fractional differential equations are established. © 2009 Elsevier Ltd. All rights reserved.
KW - Fractional integral inequalities
KW - Gronwall inequality
KW - Uniqueness and continuous dependence on parameters
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U2 - 10.1016/j.camwa.2009.05.012
DO - 10.1016/j.camwa.2009.05.012
M3 - Article
SN - 0898-1221
VL - 59
SP - 1087
EP - 1094
JO - Computers and Mathematics with Applications
JF - Computers and Mathematics with Applications
IS - 3
ER -