Investigation of the Dirac Equation by Using the Conformable Fractional Derivative

Chaos and Relativistic Energy-Momentum of the Nonlinear Time Fractional Duffing Equation

“…Converting the fractional nonlinear partial differential equation to the integer order nonlinear partial differential equation using the following conformable fractional derivative [u(x, t) = u(Θ), Θ = x + c t α α ] (for more details about this kind of derivatives see References [25][26][27][28][29]), we get:…”

“…Equations (11), (13), (22), (29), (35), (37), (40), and (91) are convergent to each other by equating the parameters in each solution.…”

The investigation of classical particle in the presence of fractional calculus

“…Different definitions of fractional derivatives can be proposed, each with remarkable properties [22][23][24][25][26], all of them valid and mathematically acceptable.…”

“…[23], in the framework of conformable fractional quantum mechanics, the threedimensional fractional harmonic oscillator is studied and by using an effective and efficient formalism, Schrödinger equation, probability density, probability flux and continuity equation have been investigated and in Ref. [24]. Fractional calculus has also been studied for the Dirac equation, the resulting wave function, and the energy eigenvalue equation.…”

The Dirac equation in a class of topologically trivial flat Gödel-type space-time backgrounds

“…The obtained eigenvalues of energy in these different classes of Gödel-type space-times are found different and the results are enough significant [71,76]. Other works are the quantum dynamics of Klein-Gordon scalar field subject to Cornell potential [82], survey on the Klein-Gordon equation in a class of Gödel-type space-times [83], the Dirac-Weyl equation in graphene under a magnetic field [84], effects of cosmic string framework on thermodynamical properties of anharmonic oscillator [85], study of bosons for three special limits of Gödel-type space-times [86], the Klein-Gordon oscillator in the presence of Cornell potential in the cosmic string space-time [87], the covariant Duffin-Kemmer-Petiau (DKP) equation in the cosmic-string space-time with interaction of a DKP field with the gravitational field produced by topological defects investigated in [88], the Klein-Gordon field in spinning cosmic string space-time with the Cornell potential [89], the relativistic spin-zero bosons in a Som-Raychaudhuri space-time investigated in [90], investigation of the Dirac equation using the conformable fractional derivative [91], effect of the Wigner-Dunkl algebra on the Dirac equation and Dirac harmonic oscillator investigated in [92], investigation of the relativistic dynamics of a Dirac field in the Som-Raychaudhuri space-time, which is described by Gödel-type metric and a stationary cylindrical symmetric solution of Einstein's field equations for a charged dust distribution in rigid rotation [93], investigation of relativistic free bosons in the Gödel-type spacetimes [94], investigation of relativistic quantum dynamics of a DKP oscillator field subject to a linear interaction in cosmic string space-time to understand the effects of gravitational fields produced by topological defects on the scalar field [95], the behaviour of relativistic spin-zero bosons in the space-time generated by a spinning cosmic string investigated in [96], relativistic spin-0 system in the presence of a Gödel-type background space-time investigated in [97], study of the Duffin-Kemmer-Petiau (DKP) equation for spin-zero bosons in the space-time generated by a cosmic string subject to a linear interaction of a DKP field with gravitational fields produced by topological defects investigated in [98], the information-theoretic measures of (1 + 1)dimensional Dirac equation in both position and momentum spaces are investigated for the trigonometric Rosen-Morse and the Morse potentials investigated in [99], analytical bound and scattering state solutions of Dirac equation for the modified deformed Hylleraas potential with a Yukawat...…”