· 2025
Fractional Differential Equations
- 20,501citations
- 2025year
Short summary
Fractional calculus, using integrals and derivatives of fractional order, is gaining traction for modeling phenomena with memory effects, offering superior tools for time-dependent effects compared to traditional integer-order calculus.
AI-generated from the title and abstract; the full text is not read.
Key points
- Fractional calculus uses integrals and derivatives of fractional order.
- It is superior to integer-order calculus for modeling time-dependent effects and memory.
- Applications include wave dynamics, financial systems, and AI.
- Finding mathematical solutions for fractional models is a key challenge.
AI-generated from the title and abstract; the full text is not read.
Abstract
In recent times, researchers across various fields have become interested in the topic of fractional calculus based on integrals and derivatives of fractional order. This area has numerous and widespread applications in fields of science and engineering, including wave and fluid dynamics, mathematical biology, financial systems, structural dynamics, robotics, and artificial intelligence, among others. Therefore, fractional models have become relevant in the context of phenomena with memory effects, in place of the conventional reliance on ordinary or partial differential equations. Fractional calculus offers superior tools for addressing time-dependent effects compared to integer-order calculus, which forms the foundation of most mathematical systems. As a result, fractional calculus is crucial to modeling real-life problems, and finding mathematical solutions is a great challenge in this regard.
The authors' abstract, as published at the source., 2025 · DOI ↗
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Field: Modeling and Simulation
Modeling and SimulationMathematics