Generalization of the Painlev\'e Property and Existence and Uniqueness in Fractional Differential Equations

TL;DR

This paper extends the Painlevé property to fractional differential equations and establishes foundational theorems on their existence and uniqueness, advancing the mathematical understanding of fractional calculus with broad scientific implications.

Contribution

It introduces a generalized Painlevé property for FDEs and proves existence and uniqueness theorems, bridging theory and applications in fractional calculus.

Findings

Extended Painlevé property to fractional differential equations

Proved existence and uniqueness theorems for linear and nonlinear FDEs

Enhanced understanding of integrability and solvability in fractional calculus

Abstract

In this paper, the Painlev\'e property to fractional differential equations (FDEs) are extended and the existence and uniqueness theorems for both linear and nonlinear FDEs are established. The results contribute to the research of integrability and solvability in the context of fractional calculus, which has significant implications in various fields such as physics, engineering, and applied sciences. By bridging the gap between pure mathematical theory and practical applications, this work provides a foundational understanding that can be utilized in modeling phenomena exhibiting memory and hereditary properties.