A new method for searching the integral solution of system of Riemann–Liouville fractional differential equations with non-instantaneous impulses

2021 ◽  
Vol 388 ◽  
pp. 113307
Author(s):  
Xian-Min Zhang
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Integral Solution ◽  
New Method ◽  
Fractional Differential

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 The fractional residual method for solving the local fractional differential equations

2020 ◽  
Vol 24 (4) ◽  
pp. 2535-2542
Author(s):  
Yong-Ju Yang
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Fractional Differential Equation ◽  
Fractional Differential Equations ◽  
Initial Solution ◽  
New Method ◽  
Residual Method ◽  
Fractional Differential ◽  
Efficiency And Reliability

This paper proposes a new method to solve local fractional differential equation. The method divides the studied equation into a system, where the initial solution is obtained from a residual equation. The new method is therefore named as the fractional residual method. Examples are given to elucidate its efficiency and reliability.

scholarly journals A new approach for solving systems of fractional differential equations via natural transform

2016 ◽  
Vol 12 (1) ◽  
pp. 5797-5804 ◽  
Author(s):  
A. S Abedl Rady ◽  
S. Z Rida ◽  
A. A. M Arafa ◽  
H. R Abedl Rahim
Keyword(s):  
Nonlinear Systems ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Variational Iteration Method ◽  
New Method ◽  
Transform Method ◽  
Variational Iteration ◽  
Fractional Differential ◽  
Linear And Nonlinear ◽  
Linear And Nonlinear Systems

In this paper, A new method proposed and coined by the authors as the natural variational iteration  transform method(NVITM) is utilized to solve linear and nonlinear systems of fractional differential equations. The new method is a combination of natural transform method and variational iteration method. The solutions of our modeled systems are calculated in the form of convergent power series with easily computable components. The numerical results shows that the approach is easy to implement and accurate when applied to various linear and nonlinear systems of fractional differential equations.

scholarly journals A new method solving local fractional differential equations in heat transfer

2019 ◽  
Vol 23 (3 Part A) ◽  
pp. 1663-1669
Author(s):  
Yong-Ju Yang
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Differential Transform Method ◽  
New Method ◽  
Transform Method ◽  
Variational Iteration ◽  
Differential Transform ◽  
Differential Operation ◽  
Fractional Differential

In this article, a new method, which is coupled by the variational iteration and reduced differential transform method, is proposed to solve local fractional differential equations. The advantage of the method is that the integral operation of variational iteration is transformed into the differential operation. One test examples is presented to demonstrate the reliability and efficiency of the proposed method.

scholarly journals The generalized Gegenbauer-Humberts wavelet for solving fractional differential equations

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 107-118
Author(s):  
Jumana Alkhalissi ◽  
Ibrahim Emiroglu ◽  
Aydin Secer ◽  
Mustafa Bayram
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Fractional Differential Equation ◽  
Fractional Differential Equations ◽  
Operational Matrix ◽  
New Method ◽  
Algebraic Equations ◽  
Non Linear ◽  
Fractional Differential ◽  
Operational Matrix Of Integration

In this paper we present a new method of wavelets, based on generalized Gegen?bauer-Humberts polynomials, named generalized Gegenbauer-Humberts wave?lets. The operational matrix of integration are derived. By using the proposed method converted linear and non-linear fractional differential equation a system of algebraic equations. In addition, discussed some examples to explain the efficiency and accuracy of the presented method.

scholarly journals The generalized Gegenbauer-Humberts wavelet for solving fractional differential equations

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 107-118
Author(s):  
Jumana Alkhalissi ◽  
Ibrahim Emiroglu ◽  
Aydin Secer ◽  
Mustafa Bayram
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Fractional Differential Equation ◽  
Fractional Differential Equations ◽  
Operational Matrix ◽  
New Method ◽  
Algebraic Equations ◽  
Non Linear ◽  
Fractional Differential ◽  
Operational Matrix Of Integration

In this paper we present a new method of wavelets, based on generalized Gegen?bauer-Humberts polynomials, named generalized Gegenbauer-Humberts wave?lets. The operational matrix of integration are derived. By using the proposed method converted linear and non-linear fractional differential equation a system of algebraic equations. In addition, discussed some examples to explain the efficiency and accuracy of the presented method.

scholarly journals An Eigenvalue-Eigenvector Method for Solving a System of Fractional Differential Equations with Uncertainty

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
M. R. Balooch Shahriyar ◽  
F. Ismail ◽  
S. Aghabeigi ◽  
A. Ahmadian ◽  
S. Salahshour
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Initial Conditions ◽  
New Method ◽  
Fractional Differential ◽  
Fuzzy Fractional Differential Equations

A new method is proposed for solving systems of fuzzy fractional differential equations (SFFDEs) with fuzzy initial conditions involving fuzzy Caputo differentiability. For this purpose, three cases are introduced based on the eigenvalue-eigenvector approach; then it is shown that the solution of system of fuzzy fractional differential equations is vector of fuzzy-valued functions. Then the method is validated by solving several examples.

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