# Solving Sequential Linear M fractional Differential Equations with Constants Coefficients

## TL;DR

This paper introduces a method for solving sequential linear fractional differential equations using the M derivative, discussing existence and uniqueness of solutions with applications to homogeneous and non-homogeneous cases.

## Contribution

It presents a novel approach for solving M fractional sequential linear differential equations with constant coefficients, including proofs of existence and uniqueness.

## Key findings

- Method effectively solves M fractional differential equations
- Existence and uniqueness of solutions are established
- Illustrations demonstrate application to various cases

## Abstract

Fractional calculus is a powerful and effective tool for modelling nonlinear systems. The M derivative is the generalization of alternative fractional derivative. This M derivative obey the properties of integer calculus. In this paper, we present the method for solving M fractional sequential linear differential equations with constant coefficients for alpha is greater than or equal to 0 and beta is greater than 0. Existence and Uniqueness of the solutions for the nth order sequential linear M fractional differential equations are discussed in detail. We have present illustration for homogeneous and non homogeneous case.