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The main objective of this paper is to obtain the fractional integral operator inequalities which provide bounds of the sum of these operators at an arbitrary point. These inequalities are derived for s-exponentially convex functions. Furthermore, a Hadamard inequality is obtained for fractional integrals by using exponentially symmetric functions. The results of this paper contain several such consequences for known fractional integrals and functions which are convex, exponentially convex, and s-convex.

This paper studies the guidance scheme for the terminal guidance problem subject to input constraints, attack angle constraints, and second-order dynamics of missile autopilot. Firstly, the guidance system model with the above multi-constraint model is given. Secondly, an anti-saturation back-stepping guidance law which makes use of the low-pass filter to avoid the differential of the virtual control signals is designed based on the terminal sliding mode method, auxiliary system, and adaptive technique. Finally, Lyapunov theory and numerical simulations are utilized to prove that the states of the system under the proposed guidance law are uniformly ultimately bounded.

In this paper, an image encryption algorithm based on the H-fractal and dynamic self-invertible matrix is proposed. The H-fractal diffusion encryption method is firstly used in this encryption algorithm. This method crosses the pixels at both ends of the H-fractal, and it can enrich the means of pixel diffusion. The encryption algorithm we propose uses the Lorenz hyperchaotic system to generate pseudorandom sequences for pixel location scrambling and self-invertible matrix construction to scramble and diffuse images. To link the cipher image with the original image, the initial values of the Lorenz hyperchaotic system are determined using the original image, and it can enhance the security of the encryption algorithm. The security analysis shows that this algorithm is easy to implement. It has a large key space and strong key sensitivity and can effectively resist plaintext attacks.

A theoretical model was developed for permeability-induced inductance variations under influences of H/E field applications in bulk composite of polycrystalline spinel ferrites and piezoelectric ceramics with coil wound around. Strain-mediated magnetization changes in ferrites facilitate the permeability variations and a significant tunability in inductance from converse magnetoelectric coupling mechanisms can be achieved as expected. Modeling the inductance variations, i.e. inductance responses with frequency, was performed in terms of thickness, frequency, Young's modulus, density as well as resonance dymanic at mechanical electromagnetic resonance frequency. From the magnetostrictive/piezoelectric constitutive equations in consideration of boundary conditions, we derive permeability expressions to allow for a quantitative description of inductance traces involved magnetic relaxation occurring around longitudinal acoustic mode in the presence of H/E field applications. The model was applied to a specific ferrite-piezoelectric tunable inductor of Ni 0.7 Zn 0.3 Ga 0.02 F e 1.98 O 4 /PZT/Ni 0.7 Zn 0.3 Ga 0.02 Fe 1.98 O 4 trilayer with coil. Then, we explicitly calculate the amplitude and tendency of inductance variations with frequency using the theory and evaluate the accordance with the corresponding experimental findings. The theory is of importance for studies on the underlying physics such field-induced permeability variations and resonance dynamics in ME tunable inductor devices. In particular, it helps to explain the recent measurements for which magnetic relaxation phenomenon occurring in typical inductance versus frequency characteristics.