Residual power series scheme treatments for fractional Klein-Gordon problem arising in soliton theory.

The Klein-Gordon problem (KGP) is one of the interesting models that appear in many scientific phenomena. These models are characterized by memory effects, which provide insight into complex phenomena in the fields of physics. In this regard, we propose a new robust algorithm called the confluent Bernoulli approach with residual power series scheme (CBCA-RPSS) to give an approximate solution for the fractional nonlinear KGP.

Spectral shifted Chebyshev collocation technique with residual power series algorithm for time fractional problems.

In this paper, two problems involving nonlinear time fractional hyperbolic partial differential equations (PDEs) and time fractional pseudo hyperbolic PDEs with nonlocal conditions are presented. Collocation technique for shifted Chebyshev of the second kind with residual power series algorithm (CTSCSK-RPSA) is the main method for solving these problems. Moreover, error analysis theory is provided in detail.