# Symmetry Analysis of Initial and Boundary Value Problems for Fractional Differential Equations in Caputo sense

## TL;DR

This paper extends Lie symmetry analysis to initial and boundary value problems involving Caputo fractional derivatives, providing new definitions, theorems, and solutions for fractional PDEs.

## Contribution

It introduces a generalized symmetry method for Caputo fractional PDEs and applies it to fractional diffusion and third-order FPDEs, offering new analytical tools.

## Key findings

- Developed generalized symmetry definitions for Caputo fractional PDEs
- Analyzed symmetry properties of fractional diffusion and third-order FPDEs
- Provided explicit solutions for specific fractional PDEs

## Abstract

In this work we study Lie symmetry analysis of initial and boundary value problems for partial differential equations (PDE) with Caputo fractional derivative. We give generalized definition and theorem for the symmetry method for PDE with Caputo fractional derivative, according to Bluman's definition and theorem for the symmetry analysis of PDE system. We investigate the symmetry analysis of initial and boundary value problem for fractional diffusion and the third order fractional partial differential equation (FPDE). Also we give some solutions.