Some new Gronwall-Bellman and Bihari type integral inequalities and its applications to Riemann-Liouville fractional differential equations
Keywords:
Gronwall-Bellman integral inequalities, Riemann-Liouville operator, Fractional Differential equations, Bihari type integral inequalitiesAbstract
In this work, we establish new variants of Gronwall–Bellman type and Bihari type integral inequalities, which serve as generalizations of some classical inequalities as well as weakly singular integral inequalities. These results provide efficient analytical tools for the qualitative study of solutions to fractional differential equations. In particular, we investigate nonlinear fractional Cauchy problems involving the Riemann–Liouville fractional derivative. Using an equivalent Volterra-type integral equation of second kind of the Cauchy problem, we analyze the dependence of solutions on initial conditions and nonlinear terms.Downloads
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