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Abstract A detailed survey of existing works on fractional-order nonlinear systems reveals the fact that practically no results exist on stability or any performance analysis of Markovian jumping fractional-order systems (FOSs) in general. The main reason is the theory of infinitesimal generator used to estimate the derivative of Lyapunov–Krasovskii Functional (LKF) is not well-developed in the fractional domain. This shortage, in theory, is focussed in this manuscript. In this work, we provide a lemma that aids in analyzing the stability of fractional-order delayed systems via integer-order derivative of LKF. Using this lemma, by constructing a new suitable LKF and employing known integral inequalities, linear matrix inequality (LMI)-based sufficient conditions that ensure stability along with H ∞/passive performance of the proposed fractional-order neural networks (FONNs) with Markovian jumping parameters are derived for the first time. Unlike the existing works, the results derived in the present study depend on the fractional order (FO) of the NNs. The importance of such order-dependent criteria is highlighted in numerical examples. Finally, the simulation results are given to show the reliability of the derived conditions.

Abstract In gas transmission networks, the pressure drop caused by friction is one of the main operation costs that is compensated through consuming energy in the compressors. In the competitive market of energy, considering the demand variation is inevitable. Hence, the power minimization should be carried out in transient state. Since the minimization problem is severely nonlinear and nonconvex subjected to nonlinear constraints, utilizing a powerful minimization tool with a straightforward procedure is very helpful. In this paper, a novel approach is proposed based on metaheuristic algorithms for power minimization of a gas transmission network in fully transient conditions. The metaheuristic algorithms, unlike the gradient dependent method, can solve the complicated minimization problem without simplification. In the proposed strategy, the cost function is not expressed explicitly as a function of minimization variables; therefore, the transient minimization can be as precise as possible. The minimization is carried out by a straightforward methodology in each time sample, which leads to more precise solutions as compared to the quasi transient minimization. The metaheuristic minimizer, called the particle swarm optimization gravitational search algorithm (PSOGSA), is utilized to find the optimum operating set points. The numerical results also confirm the accuracy and well efficiency of the proposed method.

Abstract This paper discusses the complex dynamic behavior of a novel chaotic system, which was firstly established by introducing a memristor into a similar Chen’s system. Then by choosingaas the key parameter, we analyze the stability of memristor system based on eigenvalue theory. It is also found that whenacross some critical values, the system can exhibit Neimark–Sacker bifurcation and chaos behaviors. Some numerical simulations including phase diagrams and maximum Lyapunov exponent graph of the memristor-based systems are presented to verify the existence of chaos attractors. Finally, to make the results of this paper useful in the actual situation, such as the design of chaos security algorithm, analog electronic circuit of memristor chaotic system is designed.

Abstract This manuscript prospects the controllability of Hilfer fractional neutral differential equations. The new results are obtained by implementing a suitable fixed point approach and the technique of measures of noncompactness and the outcomes and facts belong to fractional theory. Firstly, we focus the controllability and extend the discussion with nonlocal conditions. Finally, an interesting example is proposed to illustrate our main obtained results.

Abstract Conventional earthquake-resistant systems, often experience inelastic behavior in a part of the structure during a large earthquake and eventually causing residual deformation and damage to the structure. Repairing these damages are unaffordable and often leads to structure destruction. Therefore, the use of structures with the ability to focus damage on interchangeable elements, which leads to reduced earthquake damage, is very important. Due to the importance of the performance of self-centering structures to reduce their damage against various earthquakes, in this study, the Repairability Index of Post-tensioned Self-Centering Frame for Near-Field earthquake (RIPSCF-N) has been developed. According to the 12 models of the studied building, a building that can be repaired, that the maximum rotation in its connection after the earthquake does not exceed the rotation of the immediate occupancy performance. Based on this, the output data of Incremental Dynamic Analysis (IDA) in OpenSees were drawn according to the connection of relative rotation and spectral acceleration. According to the predicted performance levels of Garlock for each acceleration level, the value of the connection opening is divided by the opening of the Design Basis Earthquake (DBE) level. The resulting curve shows the repairability index according to spectral acceleration, which if less than one, the repairability target is achieved. To evaluate the damage of angles, the Angle Failure Probability of Post-tensioned Self-Centering Frame for Near-Field earthquake (AFPPSCF-N) has been developed. This index equation is determined according to the fragility curve and the intensity of damage in each building.

Abstract This paper presents a linearized finite difference scheme for solving a kind of time-space fractional nonlinear diffusion-wave equations with initial singularity, where the Caputo fractional derivative in time and the Riesz fractional derivative in space are involved. First, the considered problem is equivalently transformed into its partial integro-differential form. Then, the fully discrete scheme is constructed by using the Crank–Nicolson technique, the L1 approximation, and the convolution quadrature formula to deal with the temporal discretizations. Meanwhile, the classical central difference formula and the fractional central difference formula are applied to approximate the second-order derivative and the Riesz fractional derivative in space, respectively. Moreover, the stability and convergence of the proposed scheme are strictly proved by using the discrete energy method. Finally, some numerical experiments are presented to illustrate the theoretical results.

Abstract A numerical approach based on the shifted Chebyshev–Gauss collocation method is proposed for solving the non-linear variable-order fractional Bagley–Torvik differential equation (VO-FBTE), subject to initial and boundary conditions. The shifted fractional Chebyshev–Gauss collocation points are used as interpolation nodes, and the solution of the VO-FBTE is approximated by a truncated series of the shifted Chebyshev polynomials. The residuals are calculated at the shifted fractional Chebyshev–Gauss quadrature points. The original VO-FBTE is converted into a system of algebraic equations. The accuracy of the proposed scheme is confirmed with a set of numerical examples, and the results are compared with those obtained by other methods.

Abstract In this article, we present a novel numerical formulation for the generalized time-fractional Benjamin Bona Mohany Burgers’ (BBMB) equation using Atangana Baleanu Caputo (ABC) derivative. First, we apply a linearization technique to deal with the generalized non-linear expression, and then the Crank–Nicolson finite difference formula is used in the temporal direction. A reliable numerical technique is applied to discretize the time-fractional ABC derivative, and the central difference formulae are used to approximate the derivatives in the spatial direction. The method is shown unconditionally stable and second-order convergent in both directions through the Fourier analysis. The numerical results of two test problems are analyzed to validate the theoretical results.