Solution of Higher Order Fractional Delay Differential Equations Using Darbo Type Fixed Point Theorem

Authors

  • S. S. Handibag, M. A. Kangale, and V. E. Nikam

Keywords:

Darbo fixed point theorem, Fractional Dealy Differential Equation, Adomian Decomposition Method

Abstract

In this work, we combine measure non-compactness and generalised operators in the setting of partial order Banach spaces to provide some generalised Darbo-type fixed point theorems. We further demonstrate how our findings could potentially applied in reality by establishing that higher-order fractional delay differential equations have solutions. We back up our results with numerical
estimations based on a realistic scenario. This work explores fixed point theory in the context of partial order Banach spaces and shows how it can possibly used in real-world situations through realistic examples and facts.

References

A. Das, B. Hazarika, & P. Kumam, Some new generalization of Darbo’s fixed point theorem and its application on integral equations. Mathematics, 7(3) (2019), 214, doi:org/10.3390/math7030214.

B. C. Dhage, Partially condensing mappings in partially ordered normed linar spaces and applications to functional integral equations. Tamkang Journal of Mathematics, 45(4) (2014), 397-426, doi:org/10.5556/j.tkjm.45.2014.1512.

B. Ermentrout, & A. Mahajan, Simulating, analyzing, and animating dynamical systems: a guide to XPPAUT for researchers and students. Appl. Mech. Rev., 56(4) (2003), B53-B53, doi:org/10.1115/1.1579454.

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Published

2024-12-20

How to Cite

S. S. Handibag, M. A. Kangale, and V. E. Nikam. (2024). Solution of Higher Order Fractional Delay Differential Equations Using Darbo Type Fixed Point Theorem. Journal of Computational Analysis and Applications (JoCAAA), 33(08), 1170–1185. Retrieved from https://eudoxuspress.com/index.php/pub/article/view/1614

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