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D. Baleanu

Publications and source records attributed to D. Baleanu.

17 recordsLinked to original sources
arXiv2020

Exact Solutions of the Time Derivative Fokker-Planck Equation: A Novel Approach

In the present article, an approach to find the exact solution of the fractional Fokker-Planck equation is presented. It is based on transforming it to a system of first-order partial differential equation via Hopf transformation, together with implementing the extended unified method. On the other hand, reduction of the fractional derivatives to non autonomous ordinary derivative. Thus the fractional Fokker-Planck equation is reduced to non autonomous classical ones. Some explicit solutions of the classical, fractional time derivative Fokker-Planck equation, are obtained . It is shown that the solution of the Fokker-Planck equation is bi-Gaussian's. It is found that high friction coefficient plays a significant role in lowering the standard deviation. Further, it is found the fractionality has stronger effect than fractality. It is worthy to mention that the mixture of Gaussian's is a powerful tool in machine learning. Further, when varying the order of the fractional time derivatives, results to slight effects in the probability distribution function. Also, it is shown that the mean and mean square of the velocity vary slowly.

math.AP↗
arXiv2020

Lie group theory for nonlinear fractional K(m,n) type equation with variable coefficients

We investigated the analytical solution of fractional order K(m,n) type equation with variable coefficient which is an extended type of KdV equations into a genuinely nonlinear dispersion regime. By using the Lie symmetry analysis, we obtain the Lie point symmetries for this type of time-fractional partial differential equations (PDE). Also we present the corresponding reduced fractional differential equations (FDEs) corresponding to the time-fractional K(m,n) type equation.

math.AP↗
arXiv2019

An efficient technique for fractional modified Boussinesq and approximate long wave equations

In this paper, an efficient technique is employed to study the modified Boussinesq and approximate long wave equations of the Caputo fractional time derivative, namely q-homotopy analysis transform method. These equations are playing a vital rule in describing the properties of shallow water waves through distinct dispersion relation. The convergence analysis and error analysis has been presented in the present investigation for the future scheme. We illustrate two examples to demonstrate the leverage and effectiveness of the proposed scheme, and the error analysis has been discussed to verify the accuracy. The numerical simulation has been conducted to ensure the exactness of the future technique. The obtained numerical and graphical results are divulge, the proposed scheme is computationally very accurate and straightforward to study and find the solution for fractional coupled nonlinear complex phenomena arised in science and technology.

math.AP↗
arXiv2018

New recursive approximations for variable-order fractional operators with applications

To broaden the range of applicability of variable-order fractional differential models, reliable numerical approaches are needed to solve the model equation. In this paper, we develop Laguerre spectral collocation methods for solving variable-order fractional initial value problems on the half line. Specifically, we derive three-term recurrence relations to efficiently calculate the variable-order fractional integrals and derivatives of the modified generalized Laguerre polynomials, which lead to the corresponding fractional differentiation matrices that will be used to construct the collocation methods. Comparison with other existing methods shows the superior accuracy of the proposed spectral collocation methods.

math.NA↗
arXiv2003

Surface terms,angular momentum and Hamilton-Jacobi formalism

Quadratic Lagrangians are introduced adding surface terms to a free particle Lagrangian. Geodesic equations are used in the context of the Hamilton-Jacobi formulation of constrained sysytem. Manifold structure induced by the quadratic Lagrangian is investigated.

gr-qc↗
arXiv2003

Killing-Yano tensors and surface terms

New geometries were obtained by adding a suitable surface term involving the components of the angular momentum to the corresponding free Lagrangians. Killing vectors, Killing-Yano and Killing tensors of the obtained manifolds were investigated.

gr-qc↗
arXiv2002

Killing-Yano symmetry for a class of spacetimes admitting parallel null 1-planes

A possible generalization of plane fronted waves with parallel rays (gpp-wave) fall into a more general class of metrics admitting parallel null 1-planes. For gpp-wave metric, the zero-curvature condition is given, the Killing-Yano tensors of order two and three are found and the corresponding Killing tensors are constructed. Henceforth, the compatibility between geometric duality and non-generic symmetries is presented.

gr-qc↗
arXiv2001

Dual Metrics and Non-Generic Supersymmetries for a Class of Siklos Spacetimes

The presence of Killing-Yano tensors implies the existence of non-generic supercharges in spinning point particle theories on curved backgrounds. Dual metrics are defined through their associated non-degenerate Killing tensors of valence two. Siklos spacetimes, which are the only non-trivial Einstein spaces conformal to non-flat pp-waves are investigated in regards to the existence of their corresponding Killing and Killing-Yano tensors. It is found that under some restrictions, pp-wave metrics and Siklos spacetimes admit dual metrics and non-generic supercharges. Possible significance of those dual spacetimes are discussed.

gr-qc↗
arXiv2001

Dual Metrics for a Class of Radiative Spacetimes

Second rank non-degenerate Killing tensors for some subclasses of spacetimes admitting parallel null one-planes are investigated. Lichnérowicz radiation conditions are imposed to provide a physical meaning to spacetimes whose metrics are described through their associated second rank Killing tensors. Conditions under which the dual spacetimes retain the same physical properties are presented.

gr-qc↗
arXiv2001

Geometrization of the Lax Pair Tensors

The tensorial form of the Lax pair equations are given in a compact and geometrically transparent form in the presence of Cartan's torsion tensor. Three-dimensional spacetimes admitting Lax tensors are analyzed in detail. Solutions to Lax tensor equations include interesting examples as separable coordinates and the Toda lattice.

gr-qc↗