Fractional stochastic modeling: New approach to capture more heterogeneity

Area of Science:

• Complex Systems Modeling
• Applied Mathematics
• Computational Science

Background:

• Traditional modeling methods struggle with the inherent complexities found in nature.
• Existing fractional calculus and stochastic approaches have limitations in capturing certain natural phenomena.

Purpose of the Study:

• To propose a novel hybrid modeling approach for complex natural systems.
• To enhance the capability of capturing intricate behaviors in science, technology, and engineering.

Main Methods:

• Coupling fractional differential and integral operators with a stochastic approach.
• Testing the novel approach using systems of chaotic problems.
• Utilizing numerical simulations for validation.

Main Results:

• The hybrid approach successfully captured complex behaviors missed by individual methods.
• Numerical simulations demonstrated the efficacy of the coupled fractional-stochastic technique.
• The new method shows superior performance in modeling complex systems.

Conclusions:

• The proposed coupled fractional-stochastic approach offers a powerful new tool for modeling complex problems.
• This hybrid method is a promising future direction for scientific and engineering modeling.
• The approach enhances the ability to understand and predict complex natural phenomena.