By using the first Binet's formula the strictly completely monotonic properties of functions involving the psi and polygamma functions are obtained. As direct consequences, two inequalities are proved. As an application, the best lower and upper bounds of the nth harmonic number are established.  2005 Elsevier Inc. All rights reserved.

This paper find the most effective method to solve the time-fractional Swift-Hohenberg equation with cubicquintic non-linearity by combining the homotopy perturbation method and the fractional complex transform. The solution reveals some intermittent properties of thermal physics.

The fractional power series method is used to solve a fractional heat-like equations with variable coefficients. The solution process is elucidated, and the results show that the method is simple but effective.

we use fractional power series method (FPSM) to solve some linear or nonlinear fractional differential equations . Compared to the other method, the FPSM is more simple, derect and effective.

We will study the boundedness of Marcinkiewicz integrals with rough kernel on the generalized weighted Morrey spaces. We will also prove that the commutator operators formed by aBMORnfunction and Marcinkiewicz integrals are also bounded on the generalized weighted Morrey spaces.