Higher order numerical schemes for the solution of fractional delay differential equations

Caputo and Riemann–Liouville (R–L) are the most commonly used fractional derivative operators in the field of fractional calculus. We present here two higher-order schemes, based on R–L and Caputo definitions for the solution of fractional delay differential equations (FDDEs). For the R–L fractional derivative, interpolation-based approximation and the finite difference based approximation for Caputo fractional (C-F) derivative are employed to obtain the higher-order schemes i . e . , O h 3 − α , α ∈ ( 0 , 1 ) , the fractional order for FDDEs. For the proposed schemes the stability and error estimates are presented. The noted distinct feature is that the finite difference based approximation takes almost 50% less computation time than the interpolation-based approximation. Varied examples have been worked out to verify the efficacy of the schemes, including non-linear problems such as, the chaotic behavior occurring in the fractional order Ikeda equation, the fractional order version of the population dynamics of Lemmings and the dynamical model for sea surface temperature. • Two efficient higher order schemes are presented for solving fractional delay DEs. • One of the scheme is based on finite difference and other is interpolation based. • Stability and error estimates for both the schemes are discussed. • To verify the efficacy of the schemes, solved nonlinear and few real life problems. • Computational efficiency of both the schemes is presented.