Context. The inner disk of the young star PDS 70 may be a site of rocky planet formation, with two giant planets detected further out. Recently James Webb Space Telescope/Mid-Infrared Instrument (JWST/MIRI) Medium-Resolution Spectrometer (MRS) observations have revealed the presence of warm water vapour in the inner disk. Solids in the inner disk may inform us about the origin of this inner disk water and nature of the dust in the rocky planet-forming regions of the disk. Aims. We aim to constrain the chemical composition, lattice structure, and grain sizes of small silicate grains in the inner disk of PDS 70, observed both in JWST/MIRI MRS and the Spitzer Infrared Spectrograph ( Spitzer IRS). Methods. We used a dust fitting model, called DuCK, based on a two-layer disk model considering three different sets of dust opacities. We used Gaussian random field and distribution of hollow spheres models to obtain two sets of dust opacities using the optical constants of cosmic dust analogs derived from laboratory-based measurements. These sets take into account the grain sizes as well as their shapes. The third set of opacities was obtained from the experimentally measured transmission spectra from aerosol spectroscopy. We used stoichiometric amorphous silicates, forsterite, and enstatite in our analysis. We also studied the iron content of crystalline olivine using the resonance at 23-24 mu m and tested the presence of fayalite. Both iron-rich and magnesium-rich amorphous silicate dust species were also employed to fit the observed spectra. Results. The Gaussian random field opacity set agrees well with the observed spectrum, better than the other two opacity sets. In both MIRI and Spitzer spectra, amorphous silicates are the dominant dust species. Crystalline silicates are dominated by iron-poor olivine. The 23-24 mu m olivine band peaks at 23.44 mu m for the MIRI spectrum and 23.47 mu m for the Spitzer spectrum, representing around or less than 10 <!PCT!> of iron content in the crystalline silicate. In all of the models, we do not find strong evidence for enstatite. Moreover, the silicate band in the MIRI spectrum indicates larger grain sizes (a few microns up to 5 mu m) than the Spitzer spectrum (0.1 to 1 mu m), indicating a time-variable small grain reservoir. Conclusions. The inner PDS 70 disk is dominated by a variable reservoir of warm (T sim 350-500 K) amorphous silicates, with sim 15 <!PCT!> of forsterite in mass fraction. The 10mu m and 18mu m amorphous silicate bands are very prominent, indicating that most emission originates from optically thin dust. We suggest that the small grains detected in the PDS 70 inner disk are likely transported inward from the outer disk as a result of filtration by the pressure bump associated with the gap and fragmentation into smaller sizes at the ice line. Collisions among larger parent bodies may also contribute to the small grain reservoir in the inner disk, but these parent bodies must be enstatite-poor. In addition, the variation between MIRI and Spitzer spectra can be explained by a combination of grain growth over 15 years and a dynamical inner disk where opacity changes occur resulting from the highly variable hot (Tsim 1000 K) innermost dust reservoir.
