In this study, we considered time-fractional nonlinear telegraph equations (TFNLTEs). For solving the TFNLTEs, we deployed a method known as the Multistep Modified Reduced Differential Transform Method (MMRDTM). Prior to the multistep technique, the nonlinear term in TFNLTEs is replaced with corresponding Adomian polynomials. It can be observed that the MMRDTM is much simpler and more straightforward. On top of that, it works exceptionally where the obtained solutions are more accurately approximated over time. To demonstrate the performance of the MMRDTM in terms of its capabilities and accuracies, we provided two numerical examples of solving TFNLTEs by using MMRDTM and Modified Reduced Differential Transform Method (MRDTM). By comparing the absolute errors of the obtained solutions by both methods, we demonstrated that the solutions provided by the MMRDTM much closer to the exact solutions compared to the corresponding solutions yielded by the MRDTM. This justified that the MMRDTM provides highly accurate and precise solutions for the TFNLTEs.

This study proposed a new version of Multistep Modified Reduced Differential Transform Method (MMRDTM) which is applicable for obtaining semi-analytical approximation on Non-linear Telegraph Equations (NLTEs) with source term. Through the experimental approach, we unveiled various advantages of the proposed method, especially its ability to analytically approximate high-speed converging series. Moreover, a significant reduction in the number of calculated terms can also be observed. Before deploying the multistep technique, the substitution of non-linear term in NLTEs with the corresponding Adomian polynomial takes place. Consequently, a simpler technique for approximating NLTEs with source term was discovered. Besides that, the solutions can be estimated more precisely over a longer time. To justify our findings, solutions of NLTEs with source term are obtained using the MMRDTM. The accuracy of the proposed method for solving these equations was tested by comparing the absolute errors between the solutions obtained by the proposed method and the Modified Reduced Differential Transform Method (MRDTM) with the exact solution. The obtained solutions evidenced that the proposed MMRDTM can deliver highly precise approximations for the NLTEs with source term.

An efficient roaming service over wireless networks is essential for mobile users. It allows mobile users to seamlessly access the services provided by the home agent without losing connectivity when they visit a foreign network. This handover communication happens with the help of a foreign agent. In most cases, the communication between the mobile user and the foreign agent occurs over an unsecured channel. Therefore, researchers have proposed various authentication schemes to protect data transmitted over this unsecured channel. Most of the proposed schemes are focused on key agreement schemes. However, the key agreement schemes researchers have submitted are primarily high in computational and communication costs. Therefore, this research proposed an authenticated key agreement scheme based on passwords and smart cards with lower computational and communication costs without compromising the scheme’s security. This criterion was achieved due to using lower-cost operations and functions in the scheme. Moreover, the scheme’s development is based on the result of analyzing and improving other schemes proposed by other researchers.

In this study, we are interested in finding solutions to several porous medium equations with source terms using a new numerical approach. The general porous me In this study, we are interested in finding solutions to several porous medium equations with source terms using a new numerical approach. The general porous me