Dear Colleagues,

The fields of fractional-order quantum mechanics and systems combine concepts from fractional calculus into their modeling and design. These projects, focused on non-integer order differentiation and integration of mathematical operations, are discovered across many fields of science and engineering. Concentrating on their incorporation into quantum mechanical and electronic circuits, these ideas are being discovered to design oscillators, circuits, and control systems.

Application of B-poly basis set is used to solve fractional-order differential equations (FDEs) that modeled Schrödinger equation and electric circuits using fractional-order polynomials (α as the fractional-order of polys). The method accomplishes the desired solution in terms of continuous finite number of generalized fractional B-polys in an interval [a, b].

The focus of this research is to advance research on topics relating to the theory, project design, and application of fractional-order quantum systems and circuits. Topics of research include:

• Fractional order Forced Harmonic Oscillator (FHO);
• Fractional-order Schrödinger and Dirac equations and prediction of compacted hydrogenic orbitals (so called hydrino particles which may lead to dark matter);
• Fractional-order quantum mechanical theory, commutators;
• Exploration of atomic and molecular structure using fractional-order theory;
• Applications of fractional-order circuit models for energy storage elements, supper capacitors and batteries.

Prof. Dr. Muhammad Bhatti
Guest Editor

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