Abstract-The candidate solution in traditional Genetic Programing is evolved through prescribed number of generations using fitness measure. It has been observed that, improvement of GP on different problems is insignificant at later generations. Furthermore, GP struggles to evolve on some symbolic regression problems due to high selective pressure, where input range is very small, and few generations are allowed. In such scenarios stagnation of GP occurs and GP cannot evolve a desired solution. Recent works address these issues by using single run to reduce residual error which is based on semantic concept. A new approach is proposed called Dynamic Decomposition of Genetic Programming (DDGP) inspired by dynamic programing. DDGP decomposes a problem into sub problems and initiates sub runs in order to find sub solutions. The algebraic sum of all the sub solutions merge into an overall solution, which provides the desired solution. Experiments conducted on well known benchmarks with varying complexities, validates the proposed approach, as the empirical results of DDGP are far superior to the standard GP. Moreover, statistical analysis has been conducted using T test, which depicted significant difference on eight datasets. Symbolic regression problems where other variants of GP stagnates and cannot evolve the required solution, DDGP is highly recommended for such symbolic regression problems.

This paper is devoted to the extraction of the temporal component of the source term for the fractional diffusion-wave equation. The main features of the inverse problem are the presence of non-local damping term involving two parameter Mittag -Leffler type function and family of Samarski-Ionkin type boundary conditions. Estimates of infinite series of three parameter Mittag-Leffler type function and their convolution are established to prove the existence of the solution.

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