We construct the existence theory for generalized fractional Bessel differential equations and find solutions in form of or logarithmic power series. figure out cases when series solution is unique, non-unique, does not exist. The uniqueness theorem space Cp proved corresponding initial value problem. are concerned with following homogeneous equation $$\sum\limits_{i = 1}^m {{d_i}{x^{{\alpha _i...

In this note our aim is to present some Jordan-type inequalities for generalized Bessel functions in order to extend some recent results concerning generalized and sharp versions of the well-known Jordan’s inequality. Acknowledgements: Research partially supported by the Institute of Mathematics, University of Debrecen, Hungary. The author is grateful to Prof. Lokenath Debnath for a copy of pap...

We prove generalized Strichartz estimates for wave and massless Dirac equations in Aharonov-Bohm magnetic fields. Following a well established strategy to deal with scaling critical perturbations of dispersive PDEs, we make use Hankel transform rely on some precise Bessel functions. As complementary result, local smoothing estimate the Klein-Gordon equation same field.

and Applied Analysis 3 The convergence of the power series ∑∞ m 0 amx m seems not to guarantee the existence of solutions to the inhomogeneous Bessel differential equation 1.4 . Thus, we adopt an additional condition to ensure the existence of solutions to the equation. Theorem 2.1. Let ν be a positive nonintegral number, and let ρ be a positive constant. Assume that the radius of convergence o...

In this paper, the fast algorithms of derivatives Bessel functions with respect to parameter are obtained. Based on these algorithms, we discuss calculations related heterogeneous differential equation, such as Anger, Weber, Struve and modified functions. addition, calculation some integrals At last, numerical examples show given in paper high precision.

With the help of the generalized hyperbolic function, the subsidiary ordinary differential equation method is improved and proposed to construct exact traveling wave solutions of the nonlinear partial differential equations in a unified way. A class of nonlinear Schrödinger-type equations including the generalized Zakharov system, the Rangwala-Rao equation, and the Chen-Lee-Liu equation are inv...

A generalized single-step stepwise mutation model (SMM) is developed that takes into account an arbitrary initial state to a certain partial difference equation. This is solved in both the approximate continuum limit and the more exact discrete form. A time evolution model is developed for Y DNA or mtDNA that takes into account the reflective boundary modeling minimum microsatellite length and ...

The free vibration analysis ofhomogeneous isotropic micropolar thermoelastic cylindrical curved plate in circumferential direction has been investigated in the context of generalized themoelasticity III, recently developed by Green and Naghdi. The model has been simplified using Helmholtz decomposition technique and the resulting equations have been solved using separation of variable method. M...

We study the linearization of a class of Liénard type nonlinear second-order ordinary differential equations from the generalized Sundman transformation viewpoint. The linearizing generalized Sundman transformation for the class of equations is constructed. The transformation is used to map the underlying class of equations into a linear second-order ordinary differential equation which is not ...