2019
DOI: 10.1186/s13662-019-2187-0
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On some explicit bounds of integral inequalities related to time scales

Abstract: In this paper, we propose a new method to unify and extend some nonlinear dynamic double integral inequalities of two independent variables involving pairs of time scales via nabla derivative. The acquired results give explicit bounds which can be utilized to consider the subjective and quantitative properties of specific classes of dynamic conditions on time scales. An application to prove the validity of our established results is also given.

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Cited by 10 publications
(6 citation statements)
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References 25 publications
(16 reference statements)
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“…However, in these models, the effects of long-range memories are neglected. Recently, mathematical systems with fractional order (FO) have become more worthy than classical systems as FO models provide the description of the memory effects [17][18][19][20][21][22][23][24][25][26][27][28][29]. Owolabi et al in [30] studied local and global stability of the fractional dynamical system of prey-predator with Holling type-II involving a time delay.…”
Section: Introductionmentioning
confidence: 99%
“…However, in these models, the effects of long-range memories are neglected. Recently, mathematical systems with fractional order (FO) have become more worthy than classical systems as FO models provide the description of the memory effects [17][18][19][20][21][22][23][24][25][26][27][28][29]. Owolabi et al in [30] studied local and global stability of the fractional dynamical system of prey-predator with Holling type-II involving a time delay.…”
Section: Introductionmentioning
confidence: 99%
“…The trendy thought is to demonstrate an equation for a dynamic circumstance or a dynamic inequality wherein the area of the unknown characteristic is a presumed time scale T. The justification for considering time scales is to unify continuous and discrete inspection. Among diverse aspects of the concept, we observe that dynamic inequalities increase and unify different views of both difference and differential equations in an anticipated mode; see [19][20][21] and the references therein. Pachpatte [22] initially unifies the existing fundamental inequality where z(u, l) ≥ 0, z (u, l) ≥ 0 for r, l ∈ T and l ≤ r. Recently, Sun and Hassan [24] discovered a nonlinear integral inequality related to time scales given by…”
Section: Introductionmentioning
confidence: 84%
“…In view of their major significance and control throughout the long term, much exertion and time have been committed to the improvement and speculation of Hardy's and Copson's inequalities. However, these are not limited to the works in [5][6][7][8][9][10][11][12][13][14][15].…”
Section: Introductionmentioning
confidence: 99%