Existence and Uniqueness Theorems for Sequential Linear Conformable Fractional Differential Equations

TL;DR

This paper establishes existence and uniqueness theorems for sequential linear conformable fractional differential equations, expanding the theoretical foundation of conformable fractional calculus.

Contribution

It introduces theorems ensuring solutions' existence and uniqueness for a new class of conformable fractional differential equations.

Findings

Proved existence of solutions for sequential linear conformable fractional differential equations.

Established uniqueness conditions for solutions in conformable fractional calculus.

Extended classical differential equation results to the conformable fractional context.

Abstract

Recently, a new fractional derivative called the conformable fractional derivative is given on based basic limit definition derivative in [4]. Then, the fractional versions of chain rules, exponential functions, Gronwalls inequality, integration by parts, Taylor power series expansions is developed in [5]. In this paper, we present existence and uniqueness theorems for sequential linear conformable fractional differential equations.