Analysis of impulsive neutral Caputo fractional Volterra–Fredholm integro-differential systems with applications to Solana cryptocurrency modeling

Prabakaran Raghavendran; Yamini Parthiban; Shyamsundar Santra; Mohammadjavad Habibivostakolaei; Prabakaran Raghavendran; Yamini Parthiban; Shyamsundar Santra; Mohammadjavad Habibivostakolaei

doi:10.3934/math.20261348

AIMS Mathematics

2026, Volume 11, Issue 10: 34583-34614. doi: 10.3934/math.20261348

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Research article

Analysis of impulsive neutral Caputo fractional Volterra–Fredholm integro-differential systems with applications to Solana cryptocurrency modeling

Prabakaran Raghavendran ^{1
,},
Yamini Parthiban ^{2
,},
Shyamsundar Santra ^{3
,},
Mohammadjavad Habibivostakolaei ^{4
,
,}

1.
Center for Research, Easwari Engineering College, 18 Bharathi Salai, Ramapuram, Chennai 600089, Tamil Nadu, India; Email: rockypraba55@gmail.com
2.
Department of Mathematics, SRM Institute of Science and Technology, Ramapuram, Chennai 600089, Tamil Nadu, India; Email: yaminiparthiban.msc@gmail.com
3.
Department of Mathematics, JIS College of Engineering, Kalyani, West Bengal 741235, India; Email: shyamsundar.santra@jiscollege.ac.in
4.
Institute of Mathematics, Henan Academy of Sciences, Zhengzhou 450046, China; Email: mjhabibi@hnas.ac.cn

Received: 24 August 2026 Revised: 06 October 2026 Accepted: 19 October 2026 Published: 23 October 2026
MSC : 26A33, 34A08, 34K35, 45G10

This study investigated an impulsive neutral Volterra–Fredholm integro-differential equation (VFIDE) involving the Caputo fractional derivative and developed a mathematical framework for establishing the existence and controllability of solutions. Under appropriate assumptions on the fractional order, nonlinear functions, and integral operators, the existence of solutions was established using the Schauder fixed-point theorem, while controllability was analyzed through an admissible control formulation. The proposed model incorporates fractional memory effects, Volterra–Fredholm nonlocal interactions, and abrupt state changes through impulsive terms. A fully specified numerical example was presented using a product-integration scheme, numerical quadrature, and fixed-point iteration, with grid refinement used to examine numerical stability. The framework was further illustrated using daily Solana cryptocurrency closing-price data from January 1 to December 1, 2025. The results demonstrate the applicability of the proposed framework to fractional impulsive dynamical modeling.
- fractional differential equations,
- impulsive systems,
- Volterra–Fredholm integro-differential equations,
- controllability,
- Solana cryptocurrency
Citation: Prabakaran Raghavendran, Yamini Parthiban, Shyamsundar Santra, Mohammadjavad Habibivostakolaei. Analysis of impulsive neutral Caputo fractional Volterra–Fredholm integro-differential systems with applications to Solana cryptocurrency modeling[J]. AIMS Mathematics, 2026, 11(10): 34583-34614. doi: 10.3934/math.20261348

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Abstract

This study investigated an impulsive neutral Volterra–Fredholm integro-differential equation (VFIDE) involving the Caputo fractional derivative and developed a mathematical framework for establishing the existence and controllability of solutions. Under appropriate assumptions on the fractional order, nonlinear functions, and integral operators, the existence of solutions was established using the Schauder fixed-point theorem, while controllability was analyzed through an admissible control formulation. The proposed model incorporates fractional memory effects, Volterra–Fredholm nonlocal interactions, and abrupt state changes through impulsive terms. A fully specified numerical example was presented using a product-integration scheme, numerical quadrature, and fixed-point iteration, with grid refinement used to examine numerical stability. The framework was further illustrated using daily Solana cryptocurrency closing-price data from January 1 to December 1, 2025. The results demonstrate the applicability of the proposed framework to fractional impulsive dynamical modeling.

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