scholarly journals Vectorial Iterative Fractional Laplace Transform Method for the Analytic Solutions of Fractional Cauchy-Riemann Systems Partial Differential Equations

2020 ◽  
pp. 60-83
Author(s):  
Kebede Shigute Kenea
Keyword(s):  
Power Series ◽  
Differential Equations ◽  
Laplace Transform ◽  
Initial Conditions ◽  
Fractional Power ◽  
Power Series Solution ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Cauchy Riemann ◽  
Fractional Power Series

The present study aims to obtain infinite fractional power series solution vectors of fractional Cauchy-Riemann systems equations with initial conditions by the use of vectorial iterative fractional Laplace transform method (VIFLTM). The basic idea of the VIFLTM was developed successfully and applied to four test examples to see its effectiveness and applicability. The infinite fractional power series form solutions were successfully obtained analytically. Thus, the results show that the VIFLTM works successfully in solving fractional Cauchy-Riemann system equations with initial conditions, and hence it can be extended to other fractional differential equations.

scholarly journals Adomian Decomposition and Fractional Power Series Solution of a Class of Nonlinear Fractional Differential Equations

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 1070
Author(s):  
Pshtiwan Othman Mohammed ◽  
José António Tenreiro Machado ◽  
Juan L. G. Guirao ◽  
Ravi P. Agarwal
Keyword(s):  
Power Series ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Fractional Power ◽  
Power Series Solution ◽  
True Nature ◽  
Nonlinear Fractional Differential Equations ◽  
Adomian Decomposition ◽  
Fractional Differential ◽  
Fractional Power Series

Nonlinear fractional differential equations reflect the true nature of physical and biological models with non-locality and memory effects. This paper considers nonlinear fractional differential equations with unknown analytical solutions. The Adomian decomposition and the fractional power series methods are adopted to approximate the solutions. The two approaches are illustrated and compared by means of four numerical examples.

scholarly journals FRACTIONAL POWER SERIES APPROACH FOR THE SOLUTION OF FRACTIONAL-ORDER INTEGRO-DIFFERENTIAL EQUATIONS

Fractals ◽  
2021 ◽  
Author(s):  
MUHAMMAD AKBAR ◽  
RASHID NAWAZ ◽  
SUMBAL AHSAN ◽  
KOTTAKKARAN SOOPPY NISAR ◽  
KAMAL SHAH ◽  
...  
Keyword(s):  
Power Series ◽  
Differential Equations ◽  
Fractional Power ◽  
Power Series Method ◽  
Transform Method ◽  
Residual Power Series ◽  
Fractional Differential ◽  
Optimal Homotopy Asymptotic Method ◽  
Trigonometric Transform ◽  
Fractional Power Series

Fractional differential and integral equations are focus of the researchers owing to their tremendous applications in different field of science and technology, such as physics, chemistry, mathematical biology, dynamical system and engineering. In this work, a power series approach called Residual Power Series Method (RPSM) is applied for the solution of fractional (non-integer) order integro-differential equations (FIDEs). The Caputo sense is used for calculating fractional derivatives. Comparison of the obtained solution is made with the Trigonometric Transform Method (TTM) and Optimal Homotopy Asymptotic Method (OHAM). There is no restrictive condition on the proposed solution. The presented technique is simple in applicability and easily computable.

scholarly journals Aumann Fuzzy Improper Integral and Its Application to Solve Fuzzy Integro-Differential Equations by Laplace Transform Method

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Elhassan Eljaoui ◽  
Said Melliani ◽  
L. Saadia Chadli
Keyword(s):  
Differential Equations ◽  
Laplace Transform ◽  
Convolution Type ◽  
Convolution Product ◽  
Fuzzy Mapping ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Improper Integral ◽  
Convolution Formula

We introduce the Aumann fuzzy improper integral to define the convolution product of a fuzzy mapping and a crisp function in this paper. The Laplace convolution formula is proved in this case and used to solve fuzzy integro-differential equations with kernel of convolution type. Then, we report and correct an error in the article by Salahshour et al. dealing with the same topic.

scholarly journals Exact solution of time-fractional partial differential equations using Laplace transform

2016 ◽  
Vol 5 (1) ◽  
pp. 86
Author(s):  
Naser Al-Qutaifi
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Laplace Transform ◽  
Fractional Partial Differential Equations ◽  
Laplace Transform Method ◽  
Partial Differential ◽  
Transform Method ◽  
Integer Order ◽  
First Derivative ◽  
The Laplace Transform

<p>The idea of replacing the first derivative in time by a fractional derivative of order , where , leads to a fractional generalization of any partial differential equations of integer order. In this paper, we obtain a relationship between the solution of the integer order equation and the solution of its fractional extension by using the Laplace transform method.</p>

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.

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