Abstract. In this paper, we investigate some Gronwall type inequalities on time scales, which provide explicit bounds on unknown functions. Our results unify and extend some continuous inequalities and their corresponding discrete analogues. Two applications of the main results are given in the end of this paper.Mathematics subject classification (2010): 26D15, 26D10.
The aim of the present paper is to obtain sufficient conditions for oscillation of solutions of partial fractional differential equations with the damping term of the formTwo examples are given to illustrate the main results.
The aim of this paper is to investigate some nonlinear dynamic inequalities on time scales, which provide explicit bounds on unknown functions. The inequalities given here unify and extend some inequalities in (B G Pachpatte, On some new inequalities related to a certain inequality arising in the theory of differential equation, J. Math. Anal. Appl. 251 (2000) 736-751).
In this paper,
we study the oscillation of nonlinear fractional nabla difference equations of the form where c and α are constants,
is the Riemann–Liouville fractional nabla difference operator of order is a real number, and . Some sufficient conditions for oscillation are established.
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