Solving Conformable Fractional Differential Equations with ``EJS Software and Visualization of Sub-diffusion Process

Abstract

In this work, we numerically solve ordinary and conformable fractional differential equations using Easy Java Simulations software. Their solutions, including homogeneous and non-homogeneous parts, are compared in various time intervals. Using software’s visualization andsimulation features, we may better examine, compare, and evaluate solutions of analytical and numerical fractional differential equations. A kind of oscillatory behavior is seen in long enough times. In simulation of diffusion and sub-diffusion processes, two intriguing events have been observed.

A New Scheme for Solving a Fractional Differential Equation and a Chaotic System

“…Chaotic systems violently respond to both initial conditions and small changes in their parameters, as is well known [30]. The main goal of this research is to introduce a new approach for solving fractional differential equations [4,5,8,23,27,38,45]. Also, we study the Chaotic behavior of the studied problems.…”