Calculations of fractional derivative option pricing models based on neural network

Song, Lei; Wang, Yu; Tan, Ying; Duan, Ke

doi:10.1016/j.cam.2023.115462

Cited by 6 publications

(3 citation statements)

References 25 publications

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“…Classical fractional operators include various forms like Riemann-Liouville, Caputo, Erdelyi-Kober, Hadamard [4][5][6], and so on. These forms were frequently used in the modeling of practical problems of physical and engineering [7][8][9][10][11][12]. Recently, Kilbas et al proposed more general concepts of fractional derivatives called 𝜓-Caputo and 𝜓-Riemann-Liouville fractional derivatives [4], which unified classical definitions into a whole form by drawing into the kernel function.…”

Section: 𝑦(T)mentioning

confidence: 99%

Ground state solutions for the fractional impulsive differential system with ψ‐Caputo fractional derivative and ψ–Riemann–Liouville fractional integral

Li,

Feng

et al. 2024

Math Methods in App Sciences

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This article examines a new family of (p,q)‐Laplacian type nonlinear fractional impulsive differential coupled equations involving both the ‐Caputo fractional derivative and –Riemann–Liouville fractional integral. With the help of Nehari manifold in critical point theory and fractional calculus properties, we obtain the existence of at least one nontrivial ground state solution for the coupled system with some natural and easily verifiable superlinear conditions on the nonlinearity.

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Section: 𝑦(T)mentioning

confidence: 99%

Ground state solutions for the fractional impulsive differential system with ψ‐Caputo fractional derivative and ψ–Riemann–Liouville fractional integral

Li,

Feng

et al. 2024

Math Methods in App Sciences

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“…The applications extend to various scientific fields like spectroscopy [19], geomechanics, face recognition, and crime analysis [20]. Song et al [21], in their recent study, incorporated Neural networks into the study of fractional derivatives, wherein the authors presented a new framework for calculating fractional derivative option pricing models using neural networks. Incorporating fractional calculus into image processing [22] enables improved handling of complex image features and enhances the fidelity of image reconstruction.…”

Section: Fractional Order Applications In Multi-disciplinary Fieldsmentioning

confidence: 99%

Analyzing election trends incorporating memory effect through a fractional-order mathematical modeling

Santra,

Mahapatra

2024

Phys. Scr.

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This study proposes a new mathematical model to analyze and predict the results of a political election. In general, we predict or analyze the results using statistical methods; however, to minimize the effort of the study, we propose a fractional-order modeling approach. This study proposes a model to analyze and predict general election result trends in India, focusing on the state of West Bengal. To incorporate memory into the model, we consider the Caputo fractional derivative. The model solution's positivity, boundedness, existence, and uniqueness were tested analytically. Numerical simulations were carried out to investigate the impact of the parameters and evaluate the model's performance by incorporating the implications of the previous election for realistic situations. Following this, a qualitative analysis of the performance of political parties is discussed, and a prediction of the electoral victory is obtained.

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“…After that, fractional calculus was developed only as a pure mathematical idea for a long time. In the most recent decades, it has developed rapidly and shown versatility in different disciplines, such as viscoelasticity [1], neural network [2,3], image processing [4], anomalous diffusion [5,6], etc. Many scholars, like Fourier, Euler, Riemann, Liouville, and Hadamard, among others, made great contributions by proposing new definitions and studying significant properties for this subject.…”

Section: Introductionmentioning

confidence: 99%

New Multiplicity Results for a Boundary Value Problem Involving a ψ-Caputo Fractional Derivative of a Function with Respect to Another Function

Li,

Chen

et al. 2024

Fractal Fract

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This paper considers a nonlinear impulsive fractional boundary value problem, which involves a ψ-Caputo-type fractional derivative and integral. Combining critical point theory and fractional calculus properties, such as the semigroup laws, and relationships between the fractional integration and differentiation, new multiplicity results of infinitely many solutions are established depending on some simple algebraic conditions. Finally, examples are also presented, which show that Caputo-type fractional models can be more accurate by selecting different kernels for the fractional integral and derivative.

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Calculations of fractional derivative option pricing models based on neural network

Cited by 6 publications

References 25 publications

Ground state solutions for the fractional impulsive differential system with ψ‐Caputo fractional derivative and ψ–Riemann–Liouville fractional integral

Ground state solutions for the fractional impulsive differential system with ψ‐Caputo fractional derivative and ψ–Riemann–Liouville fractional integral

Analyzing election trends incorporating memory effect through a fractional-order mathematical modeling

New Multiplicity Results for a Boundary Value Problem Involving a ψ-Caputo Fractional Derivative of a Function with Respect to Another Function

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