The effect of deformation of special relativity by conformable derivative

Abstract

In the article, the deformation of special relativity within the frame of conformable derivative is formulated. Within this context, the two postulates of the theory were re-stated. And, the addition of velocity laws were derived and used to verify the constancy of the speed of light. The invariance principle of the laws of physics is demonstrated for some typical illustrative examples, namely, the conformable wave equation, the conformable Schrodinger equation, and the conformable Gordon-Klein equation. The current formalism may be applicable when using special relativity in a nonlinear or dispersive medium.

Solution of the Conformable Angular Equation of the Schrodinger Equation

“…This definition is a natural extension of the usual derivative and satisfies the standard properties of the traditional derivative i.e the derivative of the product and the derivative of the quotient of two functions and satisfies the chain rule. The conformable calculus has many applications in several fields, for example in physics , it was used in quantum mechanics to study The effect of fractional calculus on the formation of quantum-mechanical operators [17], and an extension of the approximate methods used in quantum mechanics was made [18][19][20], and the of conformable harmonic oscillator is quantized using the annihilation and creation operators [21], besides, the effect of deformation of special relativity studied by conformable derivative [22], and the conformable Laguerre and associated Laguerre differential equations using conformable Laplace transform are solved [23]. In this work, the conformable Schrodinger equation is separated into two parts radial which depends on the knowing the potential and angular part which we solved and we obtained the conformable spherical harmonic.…”