Oscillation Analysis for Nonlinear Discrete Fractional Order Delay and Neutral
            Equations with Forcing Term

Selvam, A. George Maria; Alzabut, Jehad; Janagaraj, R.; Adiguzel, Hakan

doi:10.46719/dsa20202929

Cited by 4 publications

(1 citation statement)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Fractional calculus is a generalization of integration and differentiation to any order. Recently, it has been realized that the fractional calculus has numerous applications in engineering, signal processing, economics and finance, probability and statistics, neural networks, and thermodynamics; see for illustrations [12][13][14][15][16] and the citations therein. In recent times, the importance has been given to fractional order calculus rather than integer order due to its applications in engineering such as neural networks, electrical and mechanical engineering, and population dynamics.…”

Section: Introductionmentioning

confidence: 99%

Oscillation of Nonlinear Fractional Dynamic Equations with Forcing Term

Manikandan

Muthulakshmi

Harikrishnan³

et al. 2021

Journal of Mathematics

View full text Add to dashboard Cite

In this paper, interval oscillation criteria for the nonlinear damped dynamic equations with forcing terms on time scales within conformable fractional derivatives are established. Our approach is determined from the implementation of generalized Riccati transformation, some properties of conformable time-scale fractional calculus, and certain mathematical inequalities. Also, we extend the study of oscillation to conformable fractional Euler-type dynamic equation. Examples are presented to emphasize the validity of the main theorems\enleadertwodots.

show abstract

Section: Introductionmentioning

confidence: 99%

Oscillation of Nonlinear Fractional Dynamic Equations with Forcing Term

Manikandan

Muthulakshmi

Harikrishnan³

et al. 2021

Journal of Mathematics

View full text Add to dashboard Cite

show abstract

Modelling Series RLC Circuit with Discrete Fractional Operator

Chatzarakis

Selvam

Janagaraj

et al. 2022

Lecture Notes in Electrical Engineering

View full text Add to dashboard Cite

Oscillation Behaviour of Solutions for a Class of a Discrete Nonlinear Fractional-Order Derivatives

Chatzarakis

Selvam

Janagaraj

et al. 2021

Tatra Mountains Mathematical Publications

View full text Add to dashboard Cite

Based on the generalized Riccati transformation technique and some inequality, we study some oscillation behaviour of solutions for a class of a discrete nonlinear fractional-order derivative equation Δ [ γ ( ℓ ) [ α ( ℓ ) + β ( ℓ ) Δ μ u ( ℓ ) ] η ] + ϕ ( ℓ ) f [ G ( ℓ ) ] = 0 , ℓ ∈ N ℓ 0 + 1 − μ , \[\Delta [\gamma (\ell ){[\alpha (\ell ) + \beta (\ell ){\Delta ^\mu }u(\ell )]^\eta }] + \phi (\ell )f[G(\ell )] = 0,\ell \in {N_{{\ell _0} + 1 - \mu }},\] where ℓ 0 > 0 , G ( ℓ ) = ∑ j = ℓ 0 ℓ − 1 + μ ( ℓ − j − 1 ) ( − μ ) u ( j ) \[{\ell _0} > 0,\quad G(\ell ) = \sum\limits_{j = {\ell _0}}^{\ell - 1 + \mu } {{{(\ell - j - 1)}^{( - \mu )}}u(j)} \] and Δ μ is the Riemann-Liouville (R-L) difference operator of the derivative of order μ, 0 < μ ≤ 1 and η is a quotient of odd positive integers. Illustrative examples are given to show the validity of the theoretical results.

show abstract

Oscillation Analysis for Nonlinear Discrete Fractional Order Delay and Neutral Equations with Forcing Term

Cited by 4 publications

References 25 publications

Oscillation of Nonlinear Fractional Dynamic Equations with Forcing Term

Oscillation of Nonlinear Fractional Dynamic Equations with Forcing Term

Modelling Series RLC Circuit with Discrete Fractional Operator

Oscillation Behaviour of Solutions for a Class of a Discrete Nonlinear Fractional-Order Derivatives

Contact Info

Product

Resources

About