Fundamental fractional exponential matrix: New computational formulae and electrical applications

Al–Zhour, Zeyad

doi:10.1016/j.aeue.2020.153557

Cited by 11 publications

(3 citation statements)

References 47 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the case of time invariance in Al‐Zhour [43], for the state transition matrix

{\Phi}_{\delta}\left(t,0\right)&amp;#x0003D;{e}&amp;#x0005E;{\bar{A}\frac{t&amp;#x0005E;{\alpha }}{\alpha }}

, there exists analytic scalar functions

{\gamma}_1(t),{\gamma}_2(t),\cdots, {\gamma}_{n-1}(t)

such that

{e}&amp;#x0005E;{\bar{A}\frac{t&amp;#x0005E;{\alpha }}{\alpha }}&amp;#x0003D;\sum \limits_{k&amp;#x0003D;0}&amp;#x0005E;{\left(l&amp;#x0002B;1\right)N}{\gamma}_k(t){\bar{A}}&amp;#x0005E;k.

…”

Section: Resultsmentioning

confidence: 99%

“…and R i , respectively; then, the matrices Ã(t), Ā(t), Bi (t), B(t), and B(t) are also independent of time, denoted as Ã, Ā, Bi , B, and B, respectively. In the case of time invariance in Al-Zhour [43], for the state transition matrix Φ 𝛿 (t, 0) = e Ā t 𝛼 𝛼 , there exists analytic scalar functions 𝛾…”

Section: Controllability Analysis Of Time-invariant Linear Quadratic ...mentioning

confidence: 99%

See 1 more Smart Citation

Controllability analysis for a class of linear quadratic conformable fractional game‐based control systems

Zhou

Chen

et al. 2023

Asian Journal of Control

View full text Add to dashboard Cite

Controllability analysis for a class of linear quadratic conformable fractional game‐based control systems (CFGBCSs) is investigated in this article. Supported by the definition and property of conformable fractional, the payoff function for linear quadratic CFGBCSs is proposed, and Nash equilibrium solution is obtained via variational method for Hamilton function correspondingly. Subsequently, the state transition matrix and controllability matrix are presented to deduce the sufficient and necessary conditions for the controllability of Nash equilibrium solution of time‐varying linear quadratic CFGBCSs and time‐invariant linear quadratic CFGBCSs, respectively. Finally, two numerical examples are furnished to justify the validity of the matrix full rank condition.

show abstract

“…In the case of time invariance in Al‐Zhour [43], for the state transition matrix

{\Phi}_{\delta}\left(t,0\right)&amp;#x0003D;{e}&amp;#x0005E;{\bar{A}\frac{t&amp;#x0005E;{\alpha }}{\alpha }}

, there exists analytic scalar functions

{\gamma}_1(t),{\gamma}_2(t),\cdots, {\gamma}_{n-1}(t)

such that

{e}&amp;#x0005E;{\bar{A}\frac{t&amp;#x0005E;{\alpha }}{\alpha }}&amp;#x0003D;\sum \limits_{k&amp;#x0003D;0}&amp;#x0005E;{\left(l&amp;#x0002B;1\right)N}{\gamma}_k(t){\bar{A}}&amp;#x0005E;k.

…”

Section: Resultsmentioning

confidence: 99%

Section: Controllability Analysis Of Time-invariant Linear Quadratic ...mentioning

confidence: 99%

Controllability analysis for a class of linear quadratic conformable fractional game‐based control systems

Zhou

Chen

et al. 2023

Asian Journal of Control

View full text Add to dashboard Cite

show abstract

“…Recently, Al-Zhour et.al. [3] studied fractional differential equations in conformable fractional derivative and obtained series solution for Laguere and Lane-Emden fractional differential equations and nonlinear dispersive PDEs [12,27]. The conformable fractional natural transform have been studied by Al-Zhour et.al.…”

Section: Introductionmentioning

confidence: 99%

On Properties of α-Sumudu Transform and Applications

2021

Punjab Univ. j. math.

View full text Add to dashboard Cite

show abstract

Exact and numerical solutions of higher-order fractional partial differential equations: A new analytical method and some applications

et al. 2022

Self Cite

View full text Add to dashboard Cite

In this paper, the solution methodology of higher-order linear fractional partial deferential equations (FPDEs) as mentioned in eqs ( 1 ) and ( 2 ) below in Caputo definition relies on a new analytical method which is called the Laplace-residual power series method (L-RPSM). The main idea of our proposed technique is to convert the original FPDE in Laplace space, and then apply the residual power series method (RPSM) by using the concept of limit to obtain the solution. Some interesting and important numerical test applications are given and discussed to illustrate the procedure of our method, and also to confirm that this method is simple, understandable and very fast for obtaining the exact and approximate solutions (ASs) of FPDEs compared with other methods such as RPSM, variational iteration method (VIM), homotopy perturbation method (HPM) and Adomian decomposition method (ADM). The main advantage of the proposed method is its simplicity in computing the coefficients of terms of series solution by using only the concept of limit at infinity and not as the other well-known analytical method such as, RPSM that need to obtain the fractional derivative (FD) each time to determine the unknown coefficients in series solutions, and VIM, ADM, or HPM that need the integration operators which is difficult in fractional case.

show abstract

Fundamental fractional exponential matrix: New computational formulae and electrical applications

Cited by 11 publications

References 47 publications

Controllability analysis for a class of linear quadratic conformable fractional game‐based control systems

Controllability analysis for a class of linear quadratic conformable fractional game‐based control systems

On Properties of α-Sumudu Transform and Applications

Exact and numerical solutions of higher-order fractional partial differential equations: A new analytical method and some applications

Contact Info

Product

Resources

About