SOME GRONWALL{BELLMAN TYPE INEQUALITIES ON TIME SCALES FOR VOLTERRA-FREDHOLM DYNAMIC INTEGRAL EQUATIONS | Zendy

Ahmed A. ElDeeb | Zendy

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SOME GRONWALL{BELLMAN TYPE INEQUALITIES ON TIME SCALES FOR VOLTERRA-FREDHOLM DYNAMIC INTEGRAL EQUATIONS

Author(s) -

Ahmed A. ElDeeb

Publication year - 2018

Publication title -

journal of the egyptian mathematical society

Language(s) - English

Resource type - Journals

eISSN - 2090-9128

pISSN - 1110-256X

DOI - 10.21608/jomes.2018.9457

Subject(s) - dynamic equation , mathematics , nonlinear system , inequality , integral equation , type (biology) , volterra integral equation , mathematical analysis , ecology , physics , quantum mechanics , biology

In this paper, we prove several new explicit estimations for the solutions of some classes of nonlinear dynamic inequalities of Gronwall–Bellman–Pachpatte type on time scales. Our results formulate some integral and discrete inequalities discussed in the literature as special cases and extend some known dynamic inequalities on time scales. The inequalities given here can be used in the analysis of the qualitative properties of certain classes of dynamic equations on time scales. Some examples are presented to demonstrate the applications of our results.

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