scholarly journals Application of the principal fractional meta-trigonometric functions for the solution of linear commensurate-order time-invariant fractional differential equations

2013 ◽  
Vol 371 (1990) ◽  
pp. 20120151 ◽  
Author(s):  
C. F. Lorenzo ◽  
T. T. Hartley ◽  
R. Malti
Keyword(s):  
Differential Equations ◽  
Laplace Transform ◽  
Fractional Differential Equations ◽  
Real World ◽  
Trigonometric Functions ◽  
Exponential Functions ◽  
Simplified Method ◽  
Fractional Differential ◽  
Time Invariant ◽  
Complex Exponential

A new and simplified method for the solution of linear constant coefficient fractional differential equations of any commensurate order is presented. The solutions are based on the R -function and on specialized Laplace transform pairs derived from the principal fractional meta-trigonometric functions. The new method simplifies the solution of such fractional differential equations and presents the solutions in the form of real functions as opposed to fractional complex exponential functions, and thus is directly applicable to real-world physics.

scholarly journals Pseudo-fractional differential equations and generalized g-Laplace transform

2021 ◽  
Vol 12 (3) ◽  
Author(s):  
J. Vanterler da C. Sousa ◽  
Rubens F. Camargo ◽  
E. Capelas de Oliveira ◽  
Gastáo S. F. Frederico
Keyword(s):  
Differential Equations ◽  
Laplace Transform ◽  
Fractional Differential Equations ◽  
Fractional Differential

scholarly journals Complete Controllability of Impulsive Fractional Linear Time-Invariant Systems with Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Xian-Feng Zhou ◽  
Song Liu ◽  
Wei Jiang
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Linear Time ◽  
Complete Controllability ◽  
Linear Time Invariant ◽  
Impulsive Fractional Differential Equations ◽  
Fractional Differential ◽  
Linear Time Invariant Systems ◽  
Time Invariant

Some flaws on impulsive fractional differential equations (systems) have been found. This paper is concerned with the complete controllability of impulsive fractional linear time-invariant dynamical systems with delay. The criteria on the controllability of the system, which is sufficient and necessary, are established by constructing suitable control inputs. Two examples are provided to illustrate the obtained results.

scholarly journals Stability analysis of linear conformable fractional differential equations system with time delays

2019 ◽  
Vol 38 (6) ◽  
pp. 159-171 ◽  
Author(s):  
Vahid Mohammadnezhad ◽  
Mostafa Eslami ◽  
Hadi Rezazadeh
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Differential Equations ◽  
Laplace Transform ◽  
Fractional Differential Equations ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Euler’S Method ◽  
Fractional Differential ◽  
Theoretical Results

In this paper, we first study stability analysis of linear conformable fractional differential equations system with time delays. Some sufficient conditions on the asymptotic stability for these systems are proposed by using properties of the fractional Laplace transform and fractional version of final value theorem. Then, we employ conformable Euler’s method to solve conformable fractional differential equations system with time delays to illustrate the effectiveness of our theoretical results

The Solution of Linear Fractional Differential Equations Using the Fractional Meta-Trigonometric Functions

2011 ◽  
Author(s):  
Carl F. Lorenzo ◽  
Rachid Malti ◽  
Tom T. Hartley
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Constant Coefficient ◽  
Laplace Transforms ◽  
New Method ◽  
Trigonometric Functions ◽  
Fractional Differential ◽  
Linear Fractional Differential Equations

A new method for the solution of linear constant coefficient fractional differential equations of any commensurate order based on the Laplace transforms of the fractional meta-trigonometric functions and the R-function is presented. The new method simplifies the solution of such equations. A simplifying characterization that reduces the number of parameters in the fractional meta-trigonometric functions is introduced.

scholarly journals On matrix fractional differential equations

2017 ◽  
Vol 9 (1) ◽  
pp. 168781401668335
Author(s):  
Adem Kılıçman ◽  
Wasan Ajeel Ahmood
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Laplace Transform ◽  
Fractional Differential Equations ◽  
Fractional Derivatives ◽  
Convolution Product ◽  
Operational Matrices ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Fractional Differential

The aim of this article is to study the matrix fractional differential equations and to find the exact solution for system of matrix fractional differential equations in terms of Riemann–Liouville using Laplace transform method and convolution product to the Riemann–Liouville fractional of matrices. Also, we show the theorem of non-homogeneous matrix fractional partial differential equation with some illustrative examples to demonstrate the effectiveness of the new methodology. The main objective of this article is to discuss the Laplace transform method based on operational matrices of fractional derivatives for solving several kinds of linear fractional differential equations. Moreover, we present the operational matrices of fractional derivatives with Laplace transform in many applications of various engineering systems as control system. We present the analytical technique for solving fractional-order, multi-term fractional differential equation. In other words, we propose an efficient algorithm for solving fractional matrix equation.

scholarly journals Conformable Laplace Transform of Fractional Differential Equations

Axioms ◽  
2018 ◽  
Vol 7 (3) ◽  
pp. 55 ◽  
Author(s):  
Fernando Silva ◽  
Davidson Moreira ◽  
Marcelo Moret
Keyword(s):  
Differential Equations ◽  
Laplace Transform ◽  
Fractional Differential Equations ◽  
Classical Model ◽  
Transform Method ◽  
Fractional Models ◽  
Constant Coefficients ◽  
Fractional Differential ◽  
Linear Differential ◽  
Fractional Orders

In this paper, we use the conformable fractional derivative to discuss some fractional linear differential equations with constant coefficients. By applying some similar arguments to the theory of ordinary differential equations, we establish a sufficient condition to guarantee the reliability of solving constant coefficient fractional differential equations by the conformable Laplace transform method. Finally, the analytical solution for a class of fractional models associated with the logistic model, the von Foerster model and the Bertalanffy model is presented graphically for various fractional orders. The solution of the corresponding classical model is recovered as a particular case.

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