Stochastic solutions of Conformable fractional Cauchy problems

TL;DR

This paper introduces stochastic solutions for conformable fractional Cauchy problems by utilizing processes with nonlinear deterministic clocks, providing a new probabilistic approach to fractional differential equations.

Contribution

It presents a novel method of solving conformable fractional Cauchy problems through stochastic processes with nonlinear clocks, expanding the toolkit for fractional differential equations.

Findings

Stochastic solutions are successfully constructed for conformable fractional Cauchy problems.

Processes with nonlinear deterministic clocks are effective in representing these solutions.

The approach offers new insights into probabilistic methods for fractional calculus.

Abstract

In this paper we give stochastic solutions of conformable fractional Cauchy problems. The stochastic solutions are obtained by running the processes corresponding to Cauchy problems with a nonlinear deterministic clock.