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 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 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>

Static Deflections and Stresses in Sandwich Beams under Various Boundary Conditions

1982 ◽  
Vol 24 (1) ◽  
pp. 11-20 ◽  
Author(s):  
S. R. Sharma ◽  
D. K. Rao
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Laplace Transform ◽  
Energy Method ◽  
Sandwich Beams ◽  
Laplace Transform Method ◽  
Transform Method ◽  
System Parameters ◽  
Various Boundary Conditions ◽  
The Laplace Transform

Expressions for deflections and stresses of sandwich beams are derived for all practically important boundary conditions for both uniform as well as concentrated loads. The energy method is used in deriving the differential equations governing deflection which are then solved by using the Laplace transform method. The influence of system parameters on deflections and stresses is illustrated for important boundary conditions by means of graphs and formulae. These investigations reveal that riveting an edge can reduce the deflections and stresses by as much as 40 per cent.

A study on the fuzzy parabolic Volterra partial integro-differential equations

2021 ◽  
Vol 40 (1) ◽  
pp. 1639-1654
Author(s):  
E. Qahremani ◽  
T. Allahviranloo ◽  
S. Abbasbandy ◽  
N. Ahmady
Keyword(s):  
Differential Equations ◽  
Laplace Transform ◽  
Existence And Uniqueness ◽  
Parabolic Type ◽  
Fuzzy Mathematics ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Differentiability Of Solutions ◽  
Fuzzy Laplace Transform ◽  
Fuzzy Solutions

This paper is concerned with aspects of the analytical fuzzy solutions of the parabolic Volterra partial integro-differential equations under generalized Hukuhara partial differentiability and it consists of two parts. The first part of this paper deals with aspects of background knowledge in fuzzy mathematics, with emphasis on the generalized Hukuhara partial differentiability. The existence and uniqueness of the solutions of the fuzzy Volterra partial integro-differential equations by considering the type of [gH - p]-differentiability of solutions are proved in this part. The second part is concerned with the central themes of this paper, using the fuzzy Laplace transform method for solving the fuzzy parabolic Volterra partial integro-differential equations with emphasis on the type of [gH - p]-differentiability of solution. We test the effectiveness of method by solving some fuzzy Volterra partial integro-differential equations of parabolic type.

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