A novel fractal-fractional order model for the understanding of an oscillatory and complex behavior of human liver with non-singular kernel

Rashid, Saima; Jarad, Fahd; Ahmad, Abdulaziz Garba

doi:10.1016/j.rinp.2022.105292

Cited by 20 publications

(7 citation statements)

References 26 publications

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“…Recently, the investigation of modified derivatives and integrals has grown in prominence in recent decades, owing to its appealing implications in a wide range of disciplines, including Maxwell fluids [1,2], circuit theory [3], and epidemics [4,5]. As an outgrowth of conventional integer analysis, fractional calculus (FC) has been exploited to examine the implications and integrals of indefinite powers.…”

Section: Introductionmentioning

confidence: 99%

An Efficient Method for Solving Fractional Black-Scholes Model with Index and Exponential Decay Kernels

Rashid

Butt

Hammouch

et al. 2022

Journal of Function Spaces

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The Black-Scholes equation (BSe) is fascinating in the business world for predicting the performance of financial investment valuation systems. The Caputo fractional derivative (CFD) and Caputo-Fabrizio fractional derivative operators are used in this research to analyze the BSe. The Adomian decomposition method (ADM) and the new iterative transform (NIM) approach are combined alongside the Yang transform. In addition, the convergence and uniqueness results for the aforementioned framework have been calculated. The existence and uniqueness results have been established and frequently accompanied innovative aspects of the prospective system in fixed point terminologies. To provide additional insight into such concepts, a variety of illustrations and tabulations are used. Additionally, the provided techniques regulate and modify the obtained analytical results in a really productive fashion, allowing us to modify and regulate the converging domains of the series solution in a pragmatic manner.

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Section: Introductionmentioning

confidence: 99%

An Efficient Method for Solving Fractional Black-Scholes Model with Index and Exponential Decay Kernels

Rashid

Butt

Hammouch

et al. 2022

Journal of Function Spaces

Self Cite

View full text Add to dashboard Cite

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“…A novel technique has been suggested in [10] to deal with nonlinear evolutionary issues. A system described as a classical integerorder di erential problem has been investigated in [11] to explore the complexities of the human liver.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Finite-Time Sliding Mode Backstepping Controller for Double-Integrator Systems with Mismatched Uncertainties and External Disturbances

Hosseinabadi

Abadi

Pota

et al. 2022

Discrete Dynamics in Nature and Society

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In this paper, a novel adaptive finite-time sliding mode backstepping (AFSMBS) control scheme is suggested to control a type of high-order double-integrator systems with mismatched disturbances and uncertainties. A robust sliding mode backstepping control method, adaptive control method, and finite-time stability notion are incorporated to provide a better tracking performance over applying them individually and to use their benefits simultaneously. The concept of a sliding mode is used to define a new form of a backstepping controller. The adaptive control method is utilized to adaptively estimate the upper bounds of the disturbances and uncertainties and the estimated data are used in the control low. The notion of the finite-time stability is incorporated with the suggested control scheme to ensure the system’s convergence within a finite time. The stability proof is obtained for the closed-loop system in a finite time utilizing the Lyapunov stability theorem. Simulation results are obtained for an example of a remotely operated vehicle (ROV) with three degrees of freedom (3-DOF) to demonstrate the efficacy of the suggested control approach.

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“…Moreover, several papers focused on the functions of bounded variation to prove some important inequalities such as the Ostrowski type [26], Simpson type [27,28], trapezoid type [29,30], and midpoint type [31]. For more applications of fractional calculus in other areas of mathematical sciences, one can consult [32][33][34][35][36][37][38][39][40][41].…”

Section: Introductionmentioning

confidence: 99%

Some New Generalized Fractional Newton’s Type Inequalities for Convex Functions

Soontharanon

Ali

Budak

et al. 2022

Journal of Function Spaces

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In this paper, we establish some new Newton’s type inequalities for differentiable convex functions using the generalized Riemann-Liouville fractional integrals. The main edge of the newly established inequalities is that these can be turned into several new and existing inequalities for different fractional integrals like Riemann-Liouville fractional integrals, k -fractional integrals, Katugampola fractional operators, conformable fractional operators, Hadamard fractional operators, and fractional operators with the exponential kernel without proving one by one. It is also shown that the newly established inequalities are the refinements of the previously established inequalities inside the literature.

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A novel fractal-fractional order model for the understanding of an oscillatory and complex behavior of human liver with non-singular kernel

Cited by 20 publications

References 26 publications

An Efficient Method for Solving Fractional Black-Scholes Model with Index and Exponential Decay Kernels

An Efficient Method for Solving Fractional Black-Scholes Model with Index and Exponential Decay Kernels

Adaptive Finite-Time Sliding Mode Backstepping Controller for Double-Integrator Systems with Mismatched Uncertainties and External Disturbances

Some New Generalized Fractional Newton’s Type Inequalities for Convex Functions

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