Advances in special functions of fractional calculus---special functions in fractional calculus and their applications in engineering (20230101), 1-38.
Subject
26 Real functions -- 26A Functions of one variable 26A33 Fractional derivatives and integrals
34 Ordinary differential equations -- 34A General theory 34A08 Fractional differential equations
34 Ordinary differential equations -- 34D Stability theory 34D06 Synchronization
Summary: ``In the present article, we have investigated the Adaptive synchronization and Anti-synchronization between fractional order 3D autonomous chaotic system and novel 3D autonomous chaotic system with quadratic exponential term using Modified adaptive control method with unknown parameters. The modified adaptive control method is very affective and more convenient in comparison to the existing method for the synchronization of the fractional order chaotic systems. The chaotic attractors and synchronization of the systems are found for fractional order time derivatives described in Caputo sense. Numerical simulation results which are carried out using Adams-Boshforth-Moulton method show that the method is reliable and effective for synchronization and anti-synchronization of autonomous chaotic systems.''