Fixed Point Theorems: Exploring Applications in Fractional Differential Equations for Economic Growth

Abdou, Afrah Ahmad Noman

doi:10.3390/fractalfract8040243

Cited by 4 publications

(1 citation statement)

References 21 publications

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“…Ansari et al [19,20] introduced some C-class functions to establish a result as an expansion of the Banach contraction principle. For a more comprehensive exploration of this topic, we direct readers to references [21][22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Fixed Point Results with Applications to Fractional Differential Equations of Anomalous Diffusion

Ma,

Zahed,

Ahmad

2024

Fractal Fract

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The main objective of this manuscript is to define the concepts of F-(⋏,h)-contraction and (α,η)-Reich type interpolative contraction in the framework of orthogonal F-metric space and prove some fixed point results. Our primary result serves as a cornerstone, from which established findings in the literature emerge as natural consequences. To enhance the clarity of our novel contributions, we furnish a significant example that not only strengthens the innovative findings but also facilitates a deeper understanding of the established theory. The concluding section of our work is dedicated to the application of these results in establishing the existence and uniqueness of a solution for a fractional differential equation of anomalous diffusion.

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Section: Introductionmentioning

confidence: 99%

Fixed Point Results with Applications to Fractional Differential Equations of Anomalous Diffusion

Ma,

Zahed,

Ahmad

2024

Fractal Fract

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Fixed-point methodologies and new investments for fuzzy fractional differential equations with approximation results

Kattan,

Hammad,

El-Sanousy

2024

Alexandria Engineering Journal

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An optimal control for non-autonomous second-order stochastic differential equations with delayed arguments

Hammad,

Kattan

2024

Phys. Scr.

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Optimal control of non-autonomous second-order stochastic differential equations with delayed arguments is indispensable for managing systems exposed to uncertainty, time-dependent dynamics, and historical influences. These equations underpin a wide range of applications, including finance, engineering, and biology, where it’s imperative to make informed decisions thatmitigate risks or maximize returns while considering the inherent randomness, evolving conditions, and the impact of past states. By employing optimal control techniques, we can devise strategies that are resilient to uncertainty, adaptable to changing circumstances, and capable of accounting for the memory effects of previous events. This empowers us to optimize system performance, bolster stability, and attain desired objectives in intricate and dynamic environments.So, the goal of this article is to introduce a novel model of second-order perturbed stochastic differential equations incorporating non-local finite delay and deviated arguments in the setting of Hilbert spaces. Moreover, essential criteria are presented to examine the existence of a mild solution and evaluate the potential for approximate and optimal control of the proposed system. These results have been obtained by using evolution operators, fixed point techniques, randomanalytic methods, and compact semigroup theory. Further, to support the theoretical results,the optimal controllability of our model was studied by considering the Lagrange problem. Finally, the results were applied to discuss the approximate controllability of a partial differential equation. These models have the potential to advance the understanding and application of optimal control techniques for a wider range of complex systems.

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Fixed Point Theorems: Exploring Applications in Fractional Differential Equations for Economic Growth

Cited by 4 publications

References 21 publications

Fixed Point Results with Applications to Fractional Differential Equations of Anomalous Diffusion

Fixed Point Results with Applications to Fractional Differential Equations of Anomalous Diffusion

Fixed-point methodologies and new investments for fuzzy fractional differential equations with approximation results

An optimal control for non-autonomous second-order stochastic differential equations with delayed arguments

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