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In this paper we study quantum (p, q)-difference equations with impulse and initial or boundary conditions. We consider first order impulsive (p, q)-difference boundary value problems and second order impulsive (p, q)-difference initial value problems. Existence and uniqueness results are proved via Banach's fixed point theorem.for first-order (p, q)-difference equations, we refer the reader to [1]. In addition, in [2], the authors defined the second-order (p, q)-difference byThen we see that if f (t) is defined on [0, T] then the function( 1.3)If f (t) = t α , α > 0, then we have the formula t 0

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In this work, CoxZn1−xFe2O4 (x = 0.0–0.4) nanoparticles (NPs) were successfully synthesized by a hydrothermal method at 200 °C for 12 h. X-ray diffraction revealed a pure cubic spinel phase of all samples with space group Fd-3m. Fourier transform infrared spectrometry disclosed the vibrational modes of metal oxides in the spinel structure. Scanning electron microscopy and transmission electron microscopy disclosed a uniform distribution of cuboidal shape NPs with a decreased average NPs size from 22.72 ± 0.62 to 20.85 ± 0.47 nm as the Co content increased. X-ray absorption near edge spectroscopy results confirmed the presence of Zn2+, Co2+ and Fe2+/Fe3+ in Co-doped samples. The pore volume, pore size and specific surface area were determined using N2 gas adsorption/desorption isotherms by the Brunauer–Emmett–Teller (BET) and Barrett–Joyner–Halenda (BJH) techniques. Electrochemical properties of supercapacitors, having active CoxZn1−xFe2O4 (x = 0.0–0.4) NPs as working electrodes, indicated pseudo-capacitor performance related to the Faradaic redox reaction. Interestingly, the highest specific capacitance (Csc), 855.33 F/g at 1 A/g, with a capacity retention of 90.41% after 1000 GCD cycle testing was achieved in the Co0.3Zn0.7Fe2O4 electrode.