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Computational approach of dynamic integral inequalities with applications to timescale calculus

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Abstract

Based on some known results and simple technique, we emphasize in this article, certain nonlinear dynamic integral inequalities in one variable on timescales. Part of the novelty herein not only unifies and extends some integral inequalities related to different cases of positive constants but also explores the explicit bounds for discontinuous functions on timescales. We contribute to the ongoing research by providing mathematical results that can be used as necessary tools in the theory of certain classes of differential, integral, finite difference and sum–difference equations on timescales. The consequences of the computational experiments show that the proposed strategy can produce adequate and reliable results. Examples are also discussed to demonstrate the importance of the tests.

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Acknowledgements

The authors are very obliged to the editor and referees for their supportive input and useful feedback.

Funding

This research was funded by the Deanship of Scientific Research at Princess Nourah Bint Abdulrahman University through the Fast-track Research Funding Program.

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Authors and Affiliations

  1. Department of Mathematics, College of Science, Princess Nourah Bint Abdulrahman University, Riyadh, Saudi Arabia

    Zareen A. Khan & Pooja Arora

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  1. Zareen A. Khan
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  2. Pooja Arora
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Correspondence to Zareen A. Khan.

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Communicated by José Tenreiro Machado.

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Khan, Z.A., Arora, P. Computational approach of dynamic integral inequalities with applications to timescale calculus. Comp. Appl. Math. 39, 273 (2020). https://doi.org/10.1007/s40314-020-01323-3

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  • DOI: https://doi.org/10.1007/s40314-020-01323-3

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