Generalized wavelet quasilinearization method for solving population growth model of fractional order

Srivástava, H. M.; Shah, Firdous A.; Irfan, Mohd

doi:10.1002/mma.6542

Cited by 27 publications

(19 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Comparative studies of the results derived by applying the various numerical and approximation methods with (for example) the available analytical or laboratory‐observed findings have been extensively and widely made in the current literature in the mathematical, physical, chemical, biological, and engineering sciences. With a view to encouraging and motivating further researches along these lines, especially with the one‐dimensional quadrature rules which we have presented in this article, we choose to cite a number of recently published works (see, for details, previous studies 16‐25 ). Indeed, as it is expected, each of these publications contains references to many earlier works which would offer further incentive and motivation for considering these worthwhile lines of future researches.…”

Section: Concluding Remarks and Observationsmentioning

confidence: 99%

Some weighted quadrature methods based upon the mean value theorems

Homeier

Srivástava

Masjed‐Jamei

et al. 2020

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

In this paper, a class of weighted quadrature methods is introduced for smooth functions based upon the use of the mean value theorems. These new quadrature rules are also treated in a systematic approach involving formal series expansion. The convergence analysis of the proposed method is studied here for both the non‐weighted and the weighted cases. Some potential areas and directions for extensions and applications of the results, which are presented in this paper, are also indicated.

show abstract

Section: Concluding Remarks and Observationsmentioning

confidence: 99%

Some weighted quadrature methods based upon the mean value theorems

Homeier

Srivástava

Masjed‐Jamei

et al. 2020

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

show abstract

“…Wavelets and wavelet transforms play an important role in various fields of science and engineering like in image processing, 1–3 biomedical engineering, 4 signal processing, 5,6 computer vision, 7,8 and so forth.…”

Section: Introductionmentioning

confidence: 99%

“…If scale and position are varied very smoothly then the transform is called continuous wavelet transform (CWT). The CWT of signal

f \in L^{2} false(ℝ false)

with respect to

ϕ \in L^{2} false(ℝ false)

is defined as 8–13

\begin{matrix} ((), W_{ϕ} f) false(b, c false) & = \int_{- \infty}^{\infty} f false(x false) \overset{ϕ_{b, c} false(x false)}{true} d x \\ = false(f * {scriptD}_{- c} ϕ false) false(b false) . \end{matrix}

…”

Section: Introductionmentioning

confidence: 99%

Wavelet transforms associated with the index Whittaker transform

Prasad

Maan

Verma

2021

Math Methods in App Sciences

View full text Add to dashboard Cite

The continuous wavelet transform (CWT) associated with the index Whittaker transform is defined and discussed using its convolution theory. Existence theorem and reconstruction formula for CWT are obtained. Moreover, composition of CWT is discussed, and its Plancherel's and Parseval's relations are also derived. Further, the discrete version of this wavelet transform and its reconstruction formula are given. Furthermore, certain properties of the discrete Whittaker wavelet transform are discussed.

show abstract

“…We turn now to the current onslaught of the Corona virus, which is referred to as COVID-19 (see, for details, [4][5][6]). As in the case of the Corona virus, the Ebola virus can be transmitted to others by contact with infected body fluids, through broken skin, or through the mucous membranes of the eyes, nose and mouth, but the Ebola virus can also be transmitted through sexual contact with a person who has the virus or has recovered from it (see, for details, [7]; see also the recently-published works [8][9][10][11] for the fractional-order modeling of various other diseases and other biological situations).…”

Section: Introduction Historical Background and Motivationmentioning

confidence: 99%

Numerical Simulation of the Fractal-Fractional Ebola Virus

Srivástava

Saad

2020

Fractal Fract

Self Cite

View full text Add to dashboard Cite

In this work we present three new models of the fractal-fractional Ebola virus. We investigate the numerical solutions of the fractal-fractional Ebola virus in the sense of three different kernels based on the power law, the exponential decay and the generalized Mittag-Leffler function by using the concepts of the fractal differentiation and fractional differentiation. These operators have two parameters: The first parameter ρ is considered as the fractal dimension and the second parameter k is the fractional order. We evaluate the numerical solutions of the fractal-fractional Ebola virus for these operators with the theory of fractional calculus and the help of the Lagrange polynomial functions. In the case of ρ=k=1, all of the numerical solutions based on the power kernel, the exponential kernel and the generalized Mittag-Leffler kernel are found to be close to each other and, therefore, one of the kernels is compared with such numerical methods as the finite difference methods. This has led to an excellent agreement. For the effect of fractal-fractional on the behavior, we study the numerical solutions for different values of ρ and k. All calculations in this work are accomplished by using the Mathematica package.

show abstract

Generalized wavelet quasilinearization method for solving population growth model of fractional order

Cited by 27 publications

References 23 publications

Some weighted quadrature methods based upon the mean value theorems

Some weighted quadrature methods based upon the mean value theorems

Wavelet transforms associated with the index Whittaker transform

Numerical Simulation of the Fractal-Fractional Ebola Virus

Contact Info

Product

Resources

About