Analysis of the Fractional-Order Kaup–Kupershmidt Equation via Novel Transforms

In this article, we develop a technique to determine the analytical result of some Kaup–Kupershmidt equations with the aid of a modified technique called the new iteration transform method. This technique is a mixture of the novel integral transformation Elzaki transformation and the new iteration technique. The nonlinear term can be handled easily by a new iteration technique. The results show that the combination of the Elzaki transformation and the new iteration technique is quite capable and basically well suited for applying in such problems and that it can be implemented to other nonlinear models. This technique is viewed as an effective alternative approach to certain existing approaches for such accurate models.

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Fractional System of Korteweg-De Vries Equations via Elzaki Transform

Mathematics ◽

10.3390/math9060673 ◽

2021 ◽

Vol 9 (6) ◽

pp. 673

Author(s):

Wenfeng He ◽

Nana Chen ◽

Ioannis Dassios ◽

Nehad Ali Shah ◽

Jae Dong Chung

Keyword(s):

Fractional Order ◽

Numerical Solutions ◽

Kdv Equation ◽

Hybrid Technique ◽

Transform Method ◽

De Vries ◽

In Series ◽

Analytical Result ◽

Approximate Result ◽

Good Agreement

In this article, a hybrid technique, called the Iteration transform method, has been implemented to solve the fractional-order coupled Korteweg-de Vries (KdV) equation. In this method, the Elzaki transform and New Iteration method are combined. The iteration transform method solutions are obtained in series form to analyze the analytical results of fractional-order coupled Korteweg-de Vries equations. To understand the analytical procedure of Iteration transform method, some numerical problems are presented for the analytical result of fractional-order coupled Korteweg-de Vries equations. It is also demonstrated that the current technique’s solutions are in good agreement with the exact results. The numerical solutions show that only a few terms are sufficient for obtaining an approximate result, which is efficient, accurate, and reliable.

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Refractory Myopic Retinal Detachment and Macular Hole Closure with Autologous Neurosensory Retinal Free Flap

Case Reports in Ophthalmology ◽

10.1159/000500275 ◽

2019 ◽

Vol 10 (2) ◽

pp. 160-164 ◽

Cited By ~ 1

Author(s):

Filipe Sousa Neves ◽

Joana Braga ◽

Paula Sepúlveda ◽

Miguel Bilhoto

Keyword(s):

Retinal Detachment ◽

Macular Hole ◽

Free Flap ◽

Vision Loss ◽

Silicone Oil ◽

Modified Technique ◽

Alternative Approach ◽

Retinal Atrophy ◽

One Year ◽

Hole Closure

The purpose of this case report is to describe a modified technique involving the use of an autologous neurosensory retinal free flap for closure of a macular hole (MH) during retinal detachment (RD) surgery. A 50-year-old female presented with sudden vision loss (light perception only) and a recurrent myopic RD associated with an MH. An autologous neurosensory retinal free flap was obtained and moved toward the MH. Silicone oil was used as an endotamponade and removed after 6 months. Two months after oil removal visual acuity improved to 20/400 and remained stable thereafter; however, the patient developed central retinal atrophy. One year after surgery the MH was closed and the retina attached. This modified technique with the use of an autologous neurosensory retinal flap provides an alternative approach for recurrent MH in RD procedures.

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A fractional-order model describing the dynamics of the novel coronavirus (COVID-19) with nonsingular kernel

Chaos Solitons & Fractals ◽

10.1016/j.chaos.2021.110859 ◽

2021 ◽

Vol 146 ◽

pp. 110859

Author(s):

Ahmed Boudaoui ◽

Yacine El hadj Moussa ◽

Zakia Hammouch ◽

Saif Ullah

Keyword(s):

Fractional Order ◽

The Novel ◽

Order Model ◽

Fractional Order Model ◽

Novel Coronavirus

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Endoscopic ultrasound-guided transgastric drainage of radiologically inaccessible left lobe liver abscess involving segment 4, caudate lobe, and left lateral segments using a modified technique

Endoscopy International Open ◽

10.1055/a-1293-7746 ◽

2021 ◽

Vol 09 (01) ◽

pp. E35-E40

Author(s):

Sharad Chandra ◽

Urvashi Chandra

Keyword(s):

Liver Abscess ◽

Open Surgery ◽

Caudate Lobe ◽

Left Lobe ◽

Ultrasound Guided ◽

Modified Technique ◽

Abscess Drainage ◽

Lateral Segment ◽

Alternative Approach ◽

Left Lateral Segment

AbstractLiver abscess requiring drainage is conventionally managed by interventional radiology-guided percutaneous drainage (PCD). Radiologically inaccessible abscesses are managed with laparoscopic or open surgery, which carries high rates of morbidity and mortality.EUS-guided transluminal liver abscess drainage is minimally invasive and can be an alternative approach for caudate lobe, segment 4, and left lateral segment abscesses. We report on three consecutive patients with radiologically inaccessible left lobe liver abscess involving the caudate lobe, segment 4, and lateral segment in whom EUS-guided transluminal drainage using a modified technique was successful.

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Central Tunicate Swarm NFOPID-Based Load Frequency Control of the Egyptian Power System Considering New Uncontrolled Wind and Photovoltaic Farms

Energies ◽

10.3390/en14123604 ◽

2021 ◽

Vol 14 (12) ◽

pp. 3604

Author(s):

Hady H. Fayek ◽

Panos Kotsampopoulos

Keyword(s):

Power System ◽

Fractional Order ◽

Frequency Control ◽

Optimization Techniques ◽

Load Frequency Control ◽

The Novel ◽

Operating Condition ◽

Load Frequency ◽

Non Linear ◽

Fractional Order Pid

This paper presents load frequency control of the 2021 Egyptian power system, which consists of multi-source electrical power generation, namely, a gas and steam combined cycle, and hydro, wind and photovoltaic power stations. The simulation model includes five generating units considering physical constraints such as generation rate constraints (GRC) and the speed governor dead band. It is assumed that a centralized controller is located at the national control center to regulate the frequency of the grid. Four controllers are applied in this research: PID, fractional-order PID (FOPID), non-linear PID (NPID) and non-linear fractional-order PID (NFOPID), to control the system frequency. The design of each controller is conducted based on the novel tunicate swarm algorithm at each operating condition. The novel method is compared to other widely used optimization techniques. The results show that the tunicate swarm NFOPID controller leads the Egyptian power system to a better performance than the other control schemes. This research also presents a comparison between four methods to self-tune the NFOPID controller at each operating condition.

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An efficient approach for solution of fractional-order Helmholtz equations

Advances in Difference Equations ◽

10.1186/s13662-020-03167-x ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Nehad Ali Shah ◽

Essam R. El-Zahar ◽

Mona D. Aljoufi ◽

Jae Dong Chung

Keyword(s):

Perturbation Method ◽

Fractional Order ◽

Homotopy Perturbation Method ◽

Hybrid Technique ◽

Science And Engineering ◽

Helmholtz Equations ◽

Transform Method ◽

Homotopy Perturbation ◽

Suggested Technique ◽

Present Technique

AbstractIn this article, a hybrid technique called the homotopy perturbation Elzaki transform method has been implemented to solve fractional-order Helmholtz equations. In the hybrid technique, the Elzaki transform method and the homotopy perturbation method are amalgamated. Three problems are solved to validate and demonstrate the efficacy of the present technique. It is also demonstrated that the results obtained from the suggested technique are in excellent agreement with the results by other techniques. It is shown that the proposed method is efficient, reliable and easy to implement for various related problems of science and engineering.

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Fractional-Order PII1/2DD1/2 Control: Theoretical Aspects and Application to a Mechatronic Axis

Applied Sciences ◽

10.3390/app11083631 ◽

2021 ◽

Vol 11 (8) ◽

pp. 3631

Author(s):

Luca Bruzzone ◽

Mario Baggetta ◽

Pietro Fanghella

Keyword(s):

Fractional Order ◽

Position Control ◽

Tracking Error ◽

Experimental Tests ◽

Maximum Torque ◽

Control Effort ◽

Tuning Method ◽

Alternative Approach ◽

Remarkable Reduction ◽

Distributed Order

Fractional Calculus is usually applied to control systems by means of the well-known PIlDm scheme, which adopts integral and derivative components of non-integer orders λ and µ. An alternative approach is to add equally distributed fractional-order terms to the PID scheme instead of replacing the integer-order terms (Distributed Order PID, DOPID). This work analyzes the properties of the DOPID scheme with five terms, that is the PII1/2DD1/2 (the half-integral and the half-derivative components are added to the classical PID). The frequency domain responses of the PID, PIlDm and PII1/2DD1/2 controllers are compared, then stability features of the PII1/2DD1/2 controller are discussed. A Bode plot-based tuning method for the PII1/2DD1/2 controller is proposed and then applied to the position control of a mechatronic axis. The closed-loop behaviours of PID and PII1/2DD1/2 are compared by simulation and by experimental tests. The results show that the PII1/2DD1/2 scheme with the proposed tuning criterium allows remarkable reduction in the position error with respect to the PID, with a similar control effort and maximum torque. For the considered mechatronic axis and trapezoidal speed law, the reduction in maximum tracking error is −71% and the reduction in mean tracking error is −77%, in correspondence to a limited increase in maximum torque (+5%) and in control effort (+4%).

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Extension of natural transform method with Daftardar-Jafari polynomials for fractional order differential equations

Alexandria Engineering Journal ◽

10.1016/j.aej.2021.01.051 ◽

2021 ◽

Vol 60 (3) ◽

pp. 3205-3217

Author(s):

Rashid Nawaz ◽

Nasir Ali ◽

Laiq Zada ◽

Kottakkkaran Sooppy Nisar ◽

M.R. Alharthi ◽

...

Keyword(s):

Differential Equations ◽

Fractional Order ◽

Transform Method ◽

Fractional Order Differential Equations

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Aboodh Transform Iterative Method for Spatial Diffusion of a Biological Population with Fractional-Order

Mathematics ◽

10.3390/math9020155 ◽

2021 ◽

Vol 9 (2) ◽

pp. 155

Author(s):

Gbenga O. Ojo ◽

Nazim I. Mahmudov

Keyword(s):

Iterative Method ◽

Fractional Order ◽

Population Model ◽

Numerical Solutions ◽

Computational Effort ◽

Spatial Diffusion ◽

Transform Method ◽

Biological Population ◽

The Laplace Transform ◽

New Iterative Method

In this paper, a new approximate analytical method is proposed for solving the fractional biological population model, the fractional derivative is described in the Caputo sense. This method is based upon the Aboodh transform method and the new iterative method, the Aboodh transform is a modification of the Laplace transform. Illustrative cases are considered and the comparison between exact solutions and numerical solutions are considered for different values of alpha. Furthermore, the surface plots are provided in order to understand the effect of the fractional order. The advantage of this method is that it is efficient, precise, and easy to implement with less computational effort.

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