On Efficient Method for System of Fractional Differential Equations

The present study introduces a new version of homotopy perturbation method for the solution of system of fractional-order differential equations. In this approach, the solution is considered as a Taylor series expansion that converges rapidly to the nonlinear problem. The systems include fractional-order stiff system, the fractional-order Genesio system, and the fractional-order matrix Riccati-type differential equation. The new approximate analytical procedure depends only on two components. Comparing the methodology with some known techniques shows that the present method is relatively easy, less computational, and highly accurate.</p

Slip Effects on Fractional Viscoelastic Fluids

Unsteady flow of an incompressible Maxwell fluid with fractional derivative induced by a sudden moved plate has been studied, where the no-slip assumption between the wall and the fluid is no longer valid. The solutions obtained for the velocity field and shear stress, written in terms of Wright generalized hypergeometric functions Ψ, by using discrete Laplace transform of the sequential fractional derivatives, satisfy all imposed initial and boundary conditions. The no-slip contributions, that appeared in the general solutions, as expected, tend to zero when slip parameter is →0. Furthermore, the solutions for ordinary Maxwell and Newtonian fluids, performing the same motion, are obtained as special cases of general solutions. The solutions for fractional and ordinary Maxwell fluid for no-slip condition also obtained as limiting cases, and they are equivalent to the previously known results. Finally, the influence of the material, slip, and the fractional parameters on the fluid motion as well as a comparison among fractional Maxwell, ordinary Maxwell, and Newtonian fluids is also discussed by graphical illustrations

Travelling waves solution for MHD aligned flow of a second grade fluid with heat transfer: A symmetry independent approach

AbstractIn this work, an approach is implemented for finding exact solutions of an incompressible MHD aligned flow with heat transfer in a second grade fluid. This approach based on travelling wave phenomenon. The partial differential equations (PDEs) are reduced to ordinary differential equations (ODEs) by using wave parameter. The methodology used in this work is independent of perturbation, symmetry consideration and other restrictive assumption. Comparison is made with the results obtained previously

Numerical Simulation Using Artificial Neural Network on Fractional Differential Equations

This chapter offers a numerical simulation of fractional differential equations by utilizing Chebyshev-simulated annealing neural network (ChSANN) and Legendre-simulated annealing neural network (LSANN). The use of Chebyshev and Legendre polynomials with simulated annealing reduces the mean square error and leads to more accurate numerical approximation. The comparison of proposed methods with previous methods confirms the accuracy of ChSANN and LSANN

Numerical study of time-fractional fourth-order differential equations with variable coefficients

AbstractIn this article, we study numerical solutions of time-fractional fourth-order partial differential equations with variable coefficients by introducing the fractional derivative in the sense of Caputo. We implement reliable series solution techniques namely Adomian decomposition method (ADM) and He’s variational iteration method (HVIM). Some applications are presented to highlight the significant features of these techniques. The comparison shows that the solutions obtained are in good agreement with each other and with their respective exact solutions. Some of these types of differential equations arise practically in the theory of transverse vibrations

Numerical Solution of System of Fractional Differential Equations in Imprecise Environment

Fractional calculus and fuzzy calculus theory, mutually, are highly applicable for showing different aspects of dynamics appearing in science. This chapter provides comprehensive discussion of system of fractional differential models in imprecise environment. In addition, presenting a new vast area to investigate numerical solutions of fuzzy fractional differential equations, numerical results of proposed system are carried out by the Grünwald‐Letnikov\u27s fractional derivative. The stability along with truncation error of the Grünwald‐Letnikov’s fractional approach is also proved. Moreover, some numerical experiments are performed and effective remarks are concluded on the basis of efficient convergence of the approximated results towards the exact solutions and on the depictions of error bar plots

Multiple-Parameter Hamiltonian Approach for Higher Accurate Approximations of a Nonlinear Oscillator with Discontinuity

We applied a new approach to obtain natural frequency of the nonlinear oscillator with discontinuity. He's Hamiltonian approach is modified for nonlinear oscillator with discontinuity for which the elastic force term is proportional to sgn(u). We employed this method for higher-order approximate solution of the nonlinear oscillator equation. This property is used to obtain approximate frequency-amplitude relationship of a nonlinear oscillator with high accuracy. Many numerical results are given to prove the efficiency of the suggested technique

A comparative analysis of machine learning approaches for plant disease identification

Background: The problems to leaf in plants are very severe and they usually shorten the lifespan of plants. Leaf diseases are mainly caused due to three types of attacks including viral, bacterial or fungal. Diseased leaves reduce the crop production and affect the agricultural economy. Since agriculture plays a vital role in the economy, thus effective mechanism is required to detect the problem in early stages.Methods: Traditional approaches used for the identification of diseased plants are based on field visits which is time consuming and tedious. In this paper a comparative analysis of machine learning approaches has been presented for the identification of healthy and non-healthy plant leaves. For experimental purpose three different types of plant leaves have been selected namely, cabbage, citrus and sorghum. In order to classify healthy and non-healthy plant leaves color based features such as pixels, statistical features such as mean, standard deviation, min, max and descriptors such as Histogram of Oriented Gradients (HOG) have been used.Results:  382 images of cabbage, 539 images of citrus and 262 images of sorghum were used as the primary dataset. The 40% data was utilized for testing and 60% were used for training which consisted of both healthy and damaged leaves. The results showed that random forest classifier is the best machine method for classification of healthy and diseased plant leaves.Conclusion:  From the extensive experimentation it is concluded that features such as color information, statistical distribution and histogram of gradients provides sufficient clue for the classification of healthy and non-healthy plants

NF-κB Inhibitors Attenuate MCAO Induced Neurodegeneration and Oxidative Stress—A Reprofiling Approach

© Copyright © 2020 Ali, Shah, Zeb, Malik, Alvi, Alkury, Rashid, Hussain, Ullah, Ullah Khan, Koh and Li. Stroke is the leading cause of morbidity and mortality worldwide. About 87% of stroke cases are ischemic, which disrupt the physiological activity of the brain, thus leading to a series of complex pathophysiological events. Despite decades of research on neuroprotectants to probe for suitable therapies against ischemic stroke, no successful results have been obtained, and new alternative approaches are urgently required in order to combat this pathological torment. To address these problems, drug repositioning/reprofiling is explored extensively. Drug repurposing aims to identify new uses for already established drugs, and this makes it an attractive commercial strategy. Nuclear factor-kappa beta (NF-κB) is reported to be involved in many physiological and pathological conditions, such as neurodegeneration, neuroinflammation, and ischemia/reperfusion (I/R) injury. In this study, we examined the neuroprotective effects of atorvastatin, cephalexin, and mycophenolate against the NF-κB in ischemic stroke, as compared to the standard NF-κB inhibitor caeffic acid phenethyl ester (CAPE). An in-silico docking analysis was performed and their potential neuroprotective activities in the in vivo transient middle cerebral artery occlusion (t-MCAO) rat model was examined. The percent (%) infarct area and 28-point composite neuro score were examined, and an immunohistochemical analysis (IHC) and enzyme-linked immunosorbent assay (ELISA) were further performed to validate the neuroprotective role of these compounds in stroke as well as their potential as antioxidants. Our results demonstrated that these novels NF-κB inhibitors could attenuate ischemic stroke-induced neuronal toxicity by targeting NF-κB, a potential therapeutic approach in ischemic stroke

Parameters Approach Applied on Nonlinear Oscillators

We applied an approach to obtain the natural frequency of the generalized Duffing oscillator u¨ + u + α3u3 + α5u5 + α7u7 + ⋯ + αnun=0 and a nonlinear oscillator with a restoring force which is the function of a noninteger power exponent of deflection u¨+αu|u|n−1=0. This approach is based on involved parameters, initial conditions, and collocation points. For any arbitrary power of n, the approximate frequency analysis is carried out between the natural frequency and amplitude. The solution procedure is simple, and the results obtained are valid for the whole solution domain