Series solution of fractional Pantograph equations via Taylor series

This article is devoted to develop a numerical approximation called Taylor minimization method for initial and boundary value fractional Pantograph equations, which governs the modelling of the train system, with neutral and multi-term delays. Taylor optimization technique is basically composed of truncated Taylor series approximation of unknown function while employment of procedure is accompanied by an optimization strategy that is simulated annealing for carrying out the learning phase of unknown Taylor series coefficients. The proposed technique is implemented on various models of Pantograph equations to study the applicability and effectiveness of the planned scheme while error analysis and comparison with previous methods are performed to validate the results. To measure the capability of convergence the data for 100 numbers of independent runs is demonstrated in the form of pictorial presentation

Modification in Hill Cipher for Cryptographic Application

To keep the information, secure from various contenders is an important factor for data security. For any organization, it is an incredibly important feature to timely transmit secured data. Optimized techniques for key management and protected encryption algorithms are always helpful for reducing the overhead of the system and maintain the integrity, authentication and confidentiality of data. Cryptographic applications play an important role in our daily lives through sending emails, exchanging bank account transaction information, through mobile communication and through ATM card transaction. To secure our information from unauthorized users, Hill Cipher is one of the most well-known symmetric cryptosystems. For Hill Cipher, here we are proposed an algorithm for encryption and decryption which is based upon the transposition, substitution and left-right shift