New Gronwall-Bellman Type Inequalities and Applications in the Analysis for Solutions to Fractional Differential Equations | Zendy

Bin Zheng | Zendy; Qinghua Feng | Zendy

Open Access

New Gronwall-Bellman Type Inequalities and Applications in the Analysis for Solutions to Fractional Differential Equations

Author(s) -

Bin Zheng,

Qinghua Feng

Publication year - 2013

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2013/705126

Subject(s) - mathematics , uniqueness , fractional calculus , type (biology) , gronwall's inequality , inequality , mathematical analysis , derivative (finance) , differential equation , ecology , financial economics , economics , biology

Some new Gronwall-Bellman type inequalities are presented in this paper. Based on these inequalities, new explicit bounds for the related unknown functions are derived. The inequalities established can also be used as a handy tool in the research of qualitative as well as quantitative analysis for solutions to some fractional differential equations defined in the sense of the modified Riemann-Liouville fractional derivative. For illustrating the validity of the results established, we present some applications for them, in which the boundedness, uniqueness, and continuous dependence on the initial value for the solutions to some certainfractional differential and integral equations are investigated

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