Solution of Fractional Telegraph Equation with Fuzzy Initial Condition

Abstract

In this work, we analyze the method of finding the solution of fractional telegraph equation of the form $ \frac{\partial^{2 \alpha} u}{\partial x^{2 \alpha}}+a \odot \frac{\partial^\alpha u}{\partial t^\alpha} +b \odot u = \frac{\partial^2 u}{\partial x^2}, $ with fuzzy initial condition, where $^C\! D$ is a Caputo fractional derivative. Comparison has been done between integer order and fractional order model. Some numerical illustrations are provided to explain the proposed theory.