FRACTIONAL POWER SERIES APPROACH FOR THE SOLUTION OF FRACTIONAL-ORDER INTEGRO-DIFFERENTIAL EQUATIONS

Fractional differential and integral equations are focus of the researchers owing to their tremendous applications in different field of science and technology, such as physics, chemistry, mathematical biology, dynamical system and engineering. In this work, a power series approach called Residual Power Series Method (RPSM) is applied for the solution of fractional (non-integer) order integro-differential equations (FIDEs). The Caputo sense is used for calculating fractional derivatives. Comparison of the obtained solution is made with the Trigonometric Transform Method (TTM) and Optimal Homotopy Asymptotic Method (OHAM). There is no restrictive condition on the proposed solution. The presented technique is simple in applicability and easily computable.

Approximate Solution of Bratu Differential Equations Using Trigonometric Basic Functions

In this paper, I have proposed a method for finding an approximate function for Bratu differential equations (BDEs), in which trigonometric basic functions are used. First, by defining trigonometric basic functions, I define the values of the transformation function in relation to trigonometric basis functions (TBFs). Following that, the approximate function is defined as a linear combination of trigonometric base functions and values of transform function which is named trigonometric transform method (TTM), and the convergence of the method is also presented. To get an approximate solution function with discrete derivatives of the solution function, we have determined the approximate solution function which satisfies in the Bratu differential equations (BDEs). In the end, the algorithm of the method is elaborated with several examples. In one example, I have presented an absolute error comparison of some approximate methods.

Reliability of Trigonometric Transform-based Multi-Carrier Scheme

This work is looking for a new physical layer of a multi-carrier wireless communication system to be implemented in low complexity way, resorting to suitable fast transform. The work presents and assesses a scheme based on Discrete Trigonometric Transform with appending symmetric redundancy either in each or multiple consecutive transformed blocks. A receiver front-end filter is proposed to enforce whole symmetry in the channel impulse response, and bank of one tap filter per sub-carrier is applied as an equalizer in the transform domain. The behaviour of the transceiver is studied in the context of practical impairments like fading channel, carrier frequency offset and narrow band interference. Moreover, the performance is evaluated in contrast with the state of art methods by means of computer simulations, and it has been found that the new scheme improves robustness and reliability of communication signal, and record lower peak to average power ratio. The study demonstrates that front-end matched filter effectively performs frequency synchronization to compensate the carrier frequency offset in the received signal.