Inequalities for m-polynomial exponentially s-type convex functions in fractional calculus

Mohammed, Pshtiwan Othman; Kashuri, Artion; Abdalla, Bahaaeldin; Hamed, Y. S.; Abualnaja, Khadijah M.

doi:10.2306/scienceasia1513-1874.2022.147

Cited by 2 publications

(1 citation statement)

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“…Fractional calculus originated in the 17th century through the work of renowned mathematicians such as L'hopital and Leibniz. It emerged as a powerful mathematical tool that extended ordinary calculus to fractional orders [15,16]. Its formalization and development gained momentum in the 19th and 20th centuries, thanks to pioneers such as Liouville, Riemann, and Grünwald.…”

Section: Introductionmentioning

confidence: 99%

Optimizing Nonlinear Variable Fractional Volta’s System Design with RBFNN-Enhanced Intelligence Computing Networks

Malik,

Bashir,

Akhtar

et al. 2024

Preprint

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The study of variable order differential operators has emerged as a powerful tool for effectively modeling nonlinear fractional differential equations and chaotic systems. In this research, we employ a nonlinear, flexible structure of radial basis function neural network (RBFNN) to model the convective flow of the generalized nonlinear Volta's system in the variable order fractional domain. The intricate physical parameters of the fractional-order system are first computed using a Variable Caputo-Fabrizio scheme, considering diverse stochastic scenarios of control constraints. Following this, we craft a parametric model using a Radial basis function neural network under various initial conditions and variable order of the generalized variable order Volta's system. We compute diverse manifestations of chaos within Volta's system using a dynamical neural network structure across different fractional order solutions. The phase portrait of the chaotic attractor demonstrates the chaotic behavior of the generalized variable order fractional Volta system through the Lyapunov exponent. We calculate time delay and embedded dimension using the Average Mutual Information (AMI) method to reconstruct the phase space for generalized variable order Volta's system. The proposed configuration of the Radial basis function neural network has been verified as an exceptionally effective tool for both soft computing and dynamics analysis of chaotic systems within the variable order fractional domain.

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Section: Introductionmentioning

confidence: 99%