Innovation is considered essential to improving competitiveness and efficiency, thereby promoting economic growth in both theory and practice. This study analyzes the impacts of innovation, measured by the number of researchers, and the number of patents and trademarks, on economic growth. The results represent issues for consideration by policymakers dealing with sustainable economic growth. Besides the literature review, an empirical analysis was undertaken using the two-step system Generalized Method of Moments (GMM). Research data was collected through the World Bank"s database, with participants from 69 developed and developing countries between 2006 and 2014. Empirical results show that innovation, together with national openness, foreign direct investment inflows, and government expenditure on education, have directly and positively influenced economic growth. In addition, the study found a positive intermediate role for institutional quality and the spillover effect of foreign direct investment in promoting the relationship between innovation and economic growth. This study suggests that policymakers should focus on improving research and development activities, strengthening economic integration, attracting foreign direct investment, and extensively reforming the institutional environment to facilitate economic development. Contribution/ Originality:This study systematically explores the role of innovation in economic growth under the influence of institutional quality and foreign direct investment, using data from 69 developed and developing countries from 2006 to 2014.

In this paper we characterize the Laplace transform of functions with power growth square averages and study several multi-term Caputo and Riemann-Liouville fractional integro-differential equations in this space of functions.

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