Solutions of Initial Value Problems with Non-Singular, Caputo Type and Riemann-Liouville Type, Integro-Differential Operators

Motivated by the recent interest in generalized fractional order operators and their applications, we consider some classes of integro-differential initial value problems based on derivatives Riemann–Liouville Caputo form, but with non-singular kernels. We show that, general, solutions to these possess discontinuities at origin. also how can be re-formulated provide that are continuous origin this imposes further constraints system. Consideration intrinsic discontinuities, or constraints, is important if they employed mathematical modelling applications.