Analysis of nonlinear time-fractional Klein-Gordon equation with power law kernel

<abstract><p>We investigate the nonlinear Klein-Gordon equation with Caputo fractional derivative. The general series solution of the system is derived by using the composition of the double Laplace transform with the decomposition method. It is noted that the obtained solution converges to the exact solution of the model. The existence of the model in the presence of Caputo fractional derivative is performed. The validity and precision of the presented method are exhibited with particular examples with suitable subsidiary conditions, where good agreements are obtained. The error analysis and its corresponding surface plots are presented for each example. From the numerical solutions, we observe that the proposed system admits soliton solutions. It is noticed that the amplitude of the wave solution increases with deviations in time, that concludes the factor $ \omega $ considerably increases the amplitude and disrupts the dispersion/nonlinearity properties, as a result, may admit the excitation in the dynamical system. We have also depicted the physical behavior that states the advancement of localized mode excitations in the system.</p></abstract>

Dirac Equation in Cosmological Inertial Frame

Dirac equation is a one order-wave equation. Wave function uses as a probability amplitude in quantum mechanics. We make Dirac Equation from wave function, Type A in cosmological inertial frame.The Dirac equation satisfy Klein-Gordon equation in cosmological inertial frame.

Klein-Gordon Equation and Wave Function in Robertson-Walker and Schwarzschild space-tim

In the general relativity theory, we find Klein-Gordon wave functions in Robertson-Walker and Schwarzschild space-time. Specially, this article is that Klein-Gordon wave equations is treated by gauge fixing equations in Robertson-Walker space-time and Schwarzschild space-time.

Klein-Gordon Equation and Wave Function for Free Particle in Rindler Space-Time

Klein-Gordon equation is a relativistic wave equation. It treats spinless particle. The wave functioncannot use as a probability amplitude. We made Klein-Gordon equation in Rindler space-time. In this paper,we make free particle’s wave function as the solution of Klein-Gordon equation in Rindler space-time.

Yukawa Potential in Klein-Gordon Equation in Cosmological Inertial Frame

We study Yukawa potential dependent about time in cosmological inertial frame. If we solve Klein-Gordon equation, we obtain Yukawa potential dependent about time in cosmological inertial frame.

Einstein-Klein-Gordon System in Higher Dimensional

In this present work, we study the Einstein equation coupled with the nonlinear Klein-Gordon equation. We obtain Ricci tensor, scalar curvature, and Einstein equation of the Einstein-Klein-Gordon system in higher dimensional. If we put D=4, our formulations reduce to the four dimensional Einstein-Klein-Gordon system.

Vibration of Yukawa Potential Dependent Time and Extended Klein-Gordon Equation in Rindler Space-Time

Atom’s nucleus force understand by Yukawa potential independent time. We study Yukawa potentialdependent about time. We make Klein-Gordon equation is satisfied by Yukawa potential dependent about time.Yukawa potential satisfy Proca equation or Klein-Gordon equation. If we represent Yukawa potentialdependent time in Rindler space-time, this Yukawa potential satisfy the extended Klein-Gordon equation inRindler space-time. We understand Yukawa force in Rindler space-time.

Quantization of Gravitational Wave by Klein-Gordon Equation

In the general relativity theory, we find gravitational matter wave by Klein-Gordon wave equation.Specially, this article is that Quantization of gravitational wave is made by Klein-Gordon wave equation. We assume this matter wave as Dark Matter.

Klein-Gordon Equation and Wave Function in Cosmological Special Theory of Relativity

In the Cosmological Special Theory of Relativity, we study energy-momentum relations, Klein-Gordon equation and wave function.