Solution of fractional autonomous ordinary differential equations

AlAhmad, R.; AlAhmad, Q.; Abdelhadi, A.

doi:10.22436/jmcs.027.01.05

Cited by 17 publications

(5 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this part, let χ, N 1 ∈ C, and (N 1 ) > 0. We shall consider the Supertrigonometric and Superhyperbolic Mittag-Leffler type functions in one parameter, as follows [23][24][25][26][27]:…”

Section: Supertrigonometric and Superhyperbolic Mittag-leffler Type F...mentioning

confidence: 99%

See 1 more Smart Citation

Stability Results and Parametric Delayed Mittag–Leffler Matrices in Symmetric Fuzzy–Random Spaces with Application

O’Regan,

Aderyani,

Saadati

et al. 2023

Symmetry

View full text Add to dashboard Cite

We introduce a matrix-valued fractional delay differential system in diverse cases and present Fox type stability results with applications of aggregated special functions. In addition we present an example showing the numerical solutions based on the second type Kudryashov method. Finally, via the method of variation of constants, and some properties of the parametric Mittag–Leffler matrices, we obtain both symmetric random and symmetric fuzzy finite-time stability results for the governing fractional delay model. A numerical example is considered to illustrate applicability of the study.

show abstract

Section: Supertrigonometric and Superhyperbolic Mittag-leffler Type F...mentioning

confidence: 99%

“…Plus, if F is a solution of the inequality (27), then F is a solution of the following inequality, for every φ > 0,…”

Section: Fox Type Stability Of (1) For Casementioning

confidence: 99%

Stability Results and Parametric Delayed Mittag–Leffler Matrices in Symmetric Fuzzy–Random Spaces with Application

O’Regan,

Aderyani,

Saadati

et al. 2023

Symmetry

View full text Add to dashboard Cite

show abstract

“…In most cases, it is hard to gain analytical solutions of these problems. Therefore, numerical approaches have to be applied for approximating the solution of FDEs [5][6][7][8][9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Solving Fractional Order Differential Equations by Using Fractional Radial Basis Function Neural Network

Javadi,

Mesgarani,

Nikan

et al. 2023

Symmetry

View full text Add to dashboard Cite

Fractional differential equations (FDEs) arising in engineering and other sciences describe nature sufficiently in terms of symmetry properties. This paper proposes a numerical technique to approximate ordinary fractional initial value problems by applying fractional radial basis function neural network. The fractional derivative used in the method is considered Riemann-Liouville type. This method is simple to implement and approximates the solution of any arbitrary point inside or outside the domain after training the ANN model. Finally, three examples are presented to show the validity and applicability of the method.

show abstract

“…Notably, the domain of nonlinear dynamics has increasingly turned its focus to fractional models, inspiring a surge of relevant research pursuits. For those intrigued by these developments, valuable insights can be gleaned from references such as [1][2][3][4][5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

On Stability of a Fractional Discrete Reaction–Diffusion Epidemic Model

Alsayyed,

Hioual,

Gharib

et al. 2023

Fractal Fract

View full text Add to dashboard Cite

This paper considers the dynamical properties of a space and time discrete fractional reaction–diffusion epidemic model, introducing a novel generalized incidence rate. The linear stability of the equilibrium solutions of the considered discrete fractional reaction–diffusion model has been carried out, and a global asymptotic stability analysis has been undertaken. We conducted a global stability analysis using a specialized Lyapunov function that captures the system’s historical data, distinguishing it from the integer-order version. This approach significantly advanced our comprehension of the complex stability properties within discrete fractional reaction–diffusion epidemic models. To substantiate the theoretical underpinnings, this paper is accompanied by numerical examples. These examples serve a dual purpose: not only do they validate the theoretical findings, but they also provide illustrations of the practical implications of the proposed discrete fractional system.

show abstract

Solution of fractional autonomous ordinary differential equations

Abstract: Autonomous differential equations of fractional order and non-singular kernel are solved. While solutions can be obtained through numerical, graphical, or analytical solutions, we seek an implicit analytical solution.

Cited by 17 publications

References 5 publications

Stability Results and Parametric Delayed Mittag–Leffler Matrices in Symmetric Fuzzy–Random Spaces with Application

Stability Results and Parametric Delayed Mittag–Leffler Matrices in Symmetric Fuzzy–Random Spaces with Application

Solving Fractional Order Differential Equations by Using Fractional Radial Basis Function Neural Network

On Stability of a Fractional Discrete Reaction–Diffusion Epidemic Model

Contact Info

Product

Resources

About