Uniqueness property of the generalized Laplace transform and computational visualization of electromagnetic waves in plasma via fractional operators

Abstract

In this paper, the extended form of the modified Atangana–Baleanu (A-B) Caputo fractional operators (FOs) is introduced and their properties and applications are demonstrated. Some fractional differential equations are formulated using the novel operators and are solved through the generalized Laplace transform. The fractional differential equations of electromagnetic waves in plasma are analyzed using the newly defined operators with applications observed in various scientific fields. The behavior of electromagnetic waves in plasma is studied for different fractional orders and parameter values and the results are presented in the form of tables as well as 2D and 3D graphs. Changes in wavelength for various domain values and fractional orders are computed based on these graphs and tables. The relationship between the newly defined operators and those existing in the literature is examined and it is concluded that the introduced operators are more generalized than the previously established ones.

Keywords

• Fractional operators
• Mittag-Leffler function
• Generalized Laplace transform
• Fractional differential equation