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A mathematical model of economic growth with fading memory and continuous distribution of delay time is suggested. This model can be considered as a generalization of the standard Keynesian macroeconomic model. To take into account the memory and gamma-distributed lag we use the Abel-type integral and integro-differential operators with the confluent hypergeometric Kummer function in the kernel. These operators allow us to propose an economic accelerator, in which the memory and lag are taken into account. The fractional differential equation, which describes the dynamics of national income in this generalized model, is suggested. The solution of this fractional differential equation is obtained in the form of series of the confluent hypergeometric Kummer functions. The asymptotic behavior of national income, which is described by this solution, is considered.

Dynamic Keynesian Model of Economic Growth with Memory and Lag