On some explicit bounds of integral inequalities related to time scales

Khan, Zareen A.

doi:10.1186/s13662-019-2187-0

Cited by 10 publications

(6 citation statements)

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%

A predator–prey model involving variable-order fractional differential equations with Mittag-Leffler kernel

et al. 2021

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This paper is about to formulate a design of predator–prey model with constant and time fractional variable order. The predator and prey act as agents in an ecosystem in this simulation. We focus on a time fractional order Atangana–Baleanu operator in the sense of Liouville–Caputo. Due to the nonlocality of the method, the predator–prey model is generated by using another FO derivative developed as a kernel based on the generalized Mittag-Leffler function. Two fractional-order systems are assumed, with and without delay. For the numerical solution of the models, we not only employ the Adams–Bashforth–Moulton method but also explore the existence and uniqueness of these schemes. We use the fixed point theorem which is useful in describing the existence of a new approach with a particular set of solutions. For the illustration, several numerical examples are added to the paper to show the effectiveness of the numerical method.

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Section: Introductionmentioning

confidence: 99%

A predator–prey model involving variable-order fractional differential equations with Mittag-Leffler kernel

et al. 2021

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“…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%

Derivation of dynamical integral inequalities based on two-dimensional time scales theory

et al. 2020

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The main goal of this paper is to set up some new estimates of a specific class of dynamic integral inequalities (DII) which are partially linear on a time scale T with two independent variables. These, from the one hand, sum up and, on the other hand, offer a helpful method for both the qualitative and quantitative study of dynamic equations on time scales. Some applications are taken into consideration to show the validity of the fundamental results.

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“…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%

Synchronization Analysis of Multiple Integral Inequalities Driven by Steklov Operator

Albalawi

Khan

2021

Fractal Fract

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We construct a subclass of Copson’s integral inequality in this article. In order to achieve this goal, we attempt to use the Steklov operator for generalizing different inequalities of the Copson type relevant to the situations ρ>1 as well as ρ<1. We demonstrate the inequalities with the guidance of basic comparison, Holder’s inequality, and the integration by parts approach. Moreover, some new variations of Hardy’s integral inequality are also presented with the utilization of Steklov operator. We also formulate many remarks and two examples to show the novelty and authenticity of our results.

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On some explicit bounds of integral inequalities related to time scales

Cited by 10 publications

References 25 publications

A predator–prey model involving variable-order fractional differential equations with Mittag-Leffler kernel

A predator–prey model involving variable-order fractional differential equations with Mittag-Leffler kernel

Derivation of dynamical integral inequalities based on two-dimensional time scales theory

Synchronization Analysis of Multiple Integral Inequalities Driven by Steklov Operator

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