At present, a high-order, reconfigurable photonic signal processor is very difficult to implement. A simple, reconfigurable photonic N-differentiator and integrator based on a unit of the dual-ring coupled Mach–Zehnder interferometer (DRMZI) is proposed first. The reconfigurability is achieved only by controlling the thermo-optic phase shifter (TO-PS) on the two improved micro-ring resonators. The device presents a wide fine-tunable differentiation order range from 0.2  ≤  N  ≤  1.7 reconfigured as a 2  ×  2 differentiator after being optimized the TO-PS and the tunable couplers (TC). If it is reconfigured as an integrator, a first-order photonic temporal integrator with 16.1 GHz 3-dB bandwidth and integration time window 38.4 ps is achieved in our design. The 4  ×  4 port DRMZI differential unit can be cascaded into k-stage to realize 0.2  ×  k  ≤  N  ≤  1.7  ×  k order differential function, theoretically approaching any large order. At the same time, the differential signals can be successfully routed to different output ports by reconfiguring the optical path in the structure. The simulation results have shown that a two-stage 4  ×  4 photonic temporal differentiator can perform more than two order differential operations, e.g., N  =  2.4. Our research can provide a reference for chip-level large-scale integrated photonic processors.