This mathematical study formulates Hadamard variable-order fractional differential equations whose order follows a random variable’s cumulative distribution function, deriving conditions for existence, uniqueness and stability.
Key findings
- Sufficient bounds involving the fractional order and nonlinear term establish well-posedness and Ulam–Hyers stability. A numerical example illustrates how piecewise-constant CDF approximation affects solutions under the theorem’s assumptions.
Why this matters globally
The framework could support models whose memory changes with a probability distribution, but computational methods, sensitivity studies and real-data validation are needed before applied value can be assessed.
Thai researcher contribution
Kanokwan Sitthithakerngkiet of King Mongkut’s University of Technology North Bangkok is the corresponding author of this fractional-equation theory work.
Limitations to consider
Piecewise-constant CDF representation is an approximation that may depend on partition choice. Only an illustrative example is provided, without convergence-rate, numerical-sensitivity or method benchmarking, and no real data or physical system validates the model.