A Novel Analytical Approach for the Solution of Fractional-Order Diffusion-Wave Equations

In the present note, a new modification of the Adomian decomposition method is developed for the solution of fractional-order diffusion-wave equations with initial and boundary value Problems. The derivatives are described in the Caputo sense. The generalized formulation of the present technique is discussed to provide an easy way of understanding. In this context, some numerical examples of fractional-order diffusion-wave equations are solved by the suggested technique. It is investigated that the solution of fractional-order diffusion-wave equations can easily be handled by using the present technique. Moreover, a graphical representation was made for the solution of three illustrative examples. The solution-graphs are presented for integer and fractional order problems. It was found that the derived and exact results are in good agreement of integer-order problems. The convergence of fractional-order solution is the focus point of the present research work. The discussed technique is considered to be the best tool for the solution of fractional-order initial-boundary value problems in science and engineering.

A protocol for the reduction of applied torque on parent vessel duringelastase-induced aneurysm formation using rabbit animal models

Endovascular therapies for intracranial aneurysms requires animal models for testing the safety andeffectiveness prior to translation to the clinic. Rabbits combined with the elastase and right commoncarotid artery (RCCA) ligation methods is currently a widely used animal model for endovascular de-vice testing. However, the injection of elastase utilizing angiocatheters may potentially exerts adversetorque to the parent vessel and the optimal aneurysm creation period has not been well investigated.In this study, we present a modification to the elastase/RCCA-ligation method by replacing the angio-catheter with a butterfly catheter. Formation of saccular aneurysms was introduced in New Zealandwhite rabbits (n=6), and were maintained for 2, 4 and 6 weeks. The formed aneurysms exhibitedan elongated geometry and were stable during the study period. We found that the modification inthe animal surgery procedure provides improved manipulation of the surgical area, prolonged injec-tion of elastase, and effective degradation of the vascular elastic lamina. Compared to the traditionalelastase/RCCA-ligation method, the present technique can more effectively reduce unwanted injury tothe parent vessel and, therefore, improved stability of the vasculature for testing the efficacy of newlydeveloped endovascular embolization devices.

Topological Charge of Soft X-ray Vortex Beam Determined by Inline Holography

A Laguerre–Gaussian (LG) vortex beam having a spiral wavefront can be characterized by its topological charge (TC). The TC gives the number of times that the beam phase passes through the interval [0, 2π] following a closed loop surrounding the propagation axis. Here, the TC of soft X-ray vortex beams is determined using the in-line holography technique, where interference between vortex waves produced from a fork grating and divergent waves from a Fresnel zone plate is observed as a holographic image. The analyses revealed the phase distributions and the TC for the LG vortex waves, which reflects topological number of the fork gratings, as well as for the Hermite–Gaussian (HG) mode waves generated from the other gratings. We also conducted a simulation of the present technique for pair annihilation of topological defects in a magnetic texture. These results may pave the way for development of probes capable of characterizing the topological numbers of magnetic defects.

A SOLITARY CONVERGENT PERIODIC SOLUTION OF THE INVERSE TRULY NONLINEAR OSCILLATOR BY MODIFIED MICKENS’ EXTENDED ITERATION PROCEDURE

The inverse truly nonlinear oscillator is the most applied in the field of computer science, information technology, physics, electrical engineering, and mechanical engineering. The solution of the inverse truly nonlinear oscillator has been obtained by modified Mickens’ extended iteration procedure. To determine the solution of the oscillator a special type of Fourier series has been used. The iterated solutions are convergent as the second, third, and fourth approximate frequencies of the oscillator show a good concurrence with the exact result. Some researchers presented the solutions of the same oscillator by applying different methods. We have compared the obtained results with some previously published results. Some of their techniques diverge at higher-order stages but the present technique is convergent there. The method is mainly illustrated in the strongly nonlinear inverse oscillator, but it can be widely applicable in other problems arising from nonlinear sciences and engineering.

Exact Solution of Space-Time Fractional Partial Differential Equations by Adomian Decomposition Method

The intention behind this paper is to achieve exact solution of one dimensional nonlinear fractional partial differential equation(NFPDE) by using Adomian decomposition method(ADM) with suitable initial value. These equations arise in gas dynamic model and heat conduction model. The results show that ADM is powerful, straightforward and relevant to solve NFPDE. To represent usefulness of present technique, solutions of some differential equations in physical models and their graphical representation are done by MATLAB software.

Highly accurate analytical solution for free vibrations of strongly nonlinear Duffing oscillator

Based on the suggested parameter, a new analytical perturbation technique is presented to obtain highly ordered accurate analytical solutions for nonlinear Duffing oscillator with nonlinearity of high order. Comparing the obtained results with the numerical and other previously published results reveals the usefulness and correctness of the present technique. It is shown that the results are valid for small and large amplitudes. Indeed, it is found that our proposed technique produces more accurate and computationally results than the rival known methods. The obtained results show the efficiency and capability of the present perturbation technique to be applied to various strongly nonlinear differential equations.

Construction of optical solitons for conformable generalized model in nonlinear media

In the current analysis, the conformable generalized Kudryashov equation of pulses propagation with power non-linearity is processed. The considered higher order equation represents a generalized mathematical model of many well-known ones in nonlinear media. A variety of multiple kinks, bi-symmetry, periodic, singular, bright and dark optical solitons are extracted via the generalized Riccati equation mapping method. Basing on the Riccati differential equation, the theoretical algorithm extracts a number of empirical solutions that do not exist in the literature. The obtained results showed that the present technique is an effective and strong tool for solving nonlinear fractional partial differential equations and produces a very large number of solutions.

Soliton solutions of nonlinear fractional differential equations with its applications in mathematical physics

Generalized Kudryashov method has been used to private type of nonlinear fractional differential equations. Firstly, we proposed a fractional complex transform to convert fractional differential equations into ordinary differential equations. Three applications were given to demonstrate the effectiveness of the present technique. As a result, abundant types of exact analytical solutions are obtained.

On the approximate solution of fractional-order Whitham–Broer–Kaup equations

In this paper, the Homotopy perturbation Laplace method is implemented to investigate the solution of fractional-order Whitham–Broer–Kaup equations. The derivative of fractional-order is described in Caputo’s sense. To show the reliability of the suggested method, the solution of certain illustrative examples are presented. The results of the suggested method are shown and explained with the help of its graphical representation. The solutions of fractional-order problems as well as integer-order problems are determined by using the present technique. It has been observed that the obtained solutions are in significant agreement with the actual solutions to the targeted problems. Computationally, it has been analyzed that the solutions at different fractional-orders have a higher rate of convergence to the solution at integer-order of the derivative. Due to the analytical analysis of the problems, this study can further modify the solution of other fractional-order problems.

Intraocular Suture Looping Technique for Flapless Four-Point Refixation of Dislocated Intraocular Lenses

Purpose. To describe a flapless/grooveless technique for four-point refixation of a dislocated intraocular lens (IOL) with four fenestrated haptics. Methods. An intraocular suture looping technique was performed with the assistance of two 27-gauge needles. A looping needle was passed into the eye through paracentesis and was used to loop both fenestrated haptics on the same side with an 8–0 polypropylene thread. A guiding needle was used to guide the looping needle out of the eye at the scleral fixation sites. After looping each pair of fenestrated haptics on nasal/temporal sides with 8–0 polypropylene sutures, the IOL was refixated by definitive knotting. The exterior suture ends were buried into the sclera without the creation of scleral flaps/grooves. Results. The technique was employed in four eyes (three patients). The mean postoperative follow-up period was 13.8 ± 2.2 months. Postoperatively, the IOLs of all the eyes remained well positioned and stable. The postoperative visual acuities of all the eyes were improved. No suture erosion, hypotony, scleral atrophy, chronic inflammation, retinal tears, and/or detachments were observed within the follow-up period. Conclusion. The present technique provides minimal surgical invasion for the transscleral refixation of a dislocated IOL with four fenestrated haptics.