A complex valued approach to the solutions of Riemann-Liouville integral, Atangana-Baleanu integral operator and non-linear Telegraph equation via fixed point method

Panda, Sumati Kumari; Abdeljawad, Thabet; Ravichandran, C.

doi:10.1016/j.chaos.2019.109439

Cited by 82 publications

(40 citation statements)

References 44 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Thus, it is meaningful to study the proposed TB model in feasible region . For the upcoming results, we suggest the readers some recent related results for the stabilities and numerical techniques given in [23][24][25][26][27][28][29].…”

Section: Lemma 22mentioning

confidence: 99%

Stability analysis of a dynamical model of tuberculosis with incomplete treatment

et al. 2020

View full text Add to dashboard Cite

A simple deterministic epidemic model for tuberculosis is addressed in this article. The impact of effective contact rate, treatment rate, and incomplete treatment versus efficient treatment is investigated. We also analyze the asymptotic behavior, spread, and possible eradication of the TB infection. It is observed that the disease transmission dynamics is characterized by the basic reproduction ratio $\Re _{0}$ ℜ 0 ; if $\Re _{0}<1$ ℜ 0 < 1 , there is only a disease-free equilibrium which is both locally and globally asymptotically stable. Moreover, for $\Re _{0}>1$ ℜ 0 > 1 , a unique positive endemic equilibrium exists which is globally asymptotically stable. The global stability of the equilibria is shown via Lyapunov function. It is also obtained that incomplete treatment of TB causes increase in disease infection while efficient treatment results in a reduction in TB. Finally, for the estimated parameters, some numerical simulations are performed to verify the analytical results. These numerical results indicate that decrease in the effective contact rate λ and increase in the treatment rate γ play a significant role in the TB infection control.

show abstract

Section: Lemma 22mentioning

confidence: 99%

Stability analysis of a dynamical model of tuberculosis with incomplete treatment

et al. 2020

View full text Add to dashboard Cite

show abstract

“…The advantage of fractional calculus over integer-order calculus is that it provides a great deal for the kind of thought and hereditary characteristics of diversified materials and methods. From the past two decades, fractional calculus has attracted research attention towards itself due to its importance in several parts of science, like physics, fluid mechanics, heat conduction [1,19,21,24,26,27,32,33,[37][38][39][40][41][42]. We can relate to the monographs [2,22,30,36] for the fundamentals and to [4,44,45] for the current developments in the field of fractional calculus.…”

Section: Introductionmentioning

confidence: 99%

Existence of solutions of non-autonomous fractional differential equations with integral impulse condition

Kumar¹,

Chauhan

Ravichandran³

et al. 2020

Adv Differ Equ

Self Cite

View full text Add to dashboard Cite

show abstract

“…Although the literature reveals a growing interest in the area of numerical methods for PDE [29][30][31]; Wavelets gained much attention and significance in the literature of numerical simulations in the last few decades. Different types of wavelets utilized by different authors for the numerical simulation of PDEs, ODEs, fractional order ODEs, fractional-order PDEs, delay and fractional delay PDEs and integral equations [32][33][34][35][36][37][38].…”

Section: Introductionmentioning

confidence: 99%

A Haar wavelet collocation approach for solving one and two‐dimensional second‐order linear and nonlinear hyperbolic telegraph equations

Asif

Haider

Al‐Mdallal

et al. 2020

Numerical Methods Partial

View full text Add to dashboard Cite

We have developed a new numerical method based on Haar wavelet (HW) in this article for the numerical solution (NS) of one-and two-dimensional hyperbolic Telegraph equations (HTEs). The proposed technique is utilized for one-and two-dimensional linear and nonlinear problems, which shows its advantage over other existing numerical methods. In this technique, we approximated both space and temporal derivatives by the truncated Haar series. The algorithm of the method is simple and we can implement easily in any other programming language. The technique is tested on some linear and nonlinear examples from literature. The maximum absolute errors (MAEs), root mean square errors (RMSEs), and computational convergence rate are calculated for different number of collocation points (CPs) and also some 3D graphs are also drawn. The results show that the proposed technique is simply applicable and accurate.

show abstract

A complex valued approach to the solutions of Riemann-Liouville integral, Atangana-Baleanu integral operator and non-linear Telegraph equation via fixed point method

Cited by 82 publications

References 44 publications

Stability analysis of a dynamical model of tuberculosis with incomplete treatment

Stability analysis of a dynamical model of tuberculosis with incomplete treatment

Existence of solutions of non-autonomous fractional differential equations with integral impulse condition

A Haar wavelet collocation approach for solving one and two‐dimensional second‐order linear and nonlinear hyperbolic telegraph equations

Contact Info

Product

Resources

About