Solving multi-dimensional fractional integro-differential equations with the initial and boundary conditions by using multi-dimensional Laplace Transform method

2017 ◽  
Vol 10 (1) ◽  
pp. 105-115
Author(s):  
Adem Kılıçman ◽  
Wasan Ajeel Ahmood
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Laplace Transform ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Initial And Boundary Conditions

scholarly journals Effects of radiation and magnetohydrodynamic on unsteady Casson fluid over accelerated plate

2021 ◽  
Vol 85 (1) ◽  
pp. 93-100
Author(s):  
Nur Fatihah Mod Omar ◽  
Husna Izzati Osman ◽  
Ahmad Qushairi Mohamad ◽  
Rahimah Jusoh ◽  
Zulkhibri Ismail
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Casson Fluid ◽  
Dimensionless Form ◽  
Laplace Transform Method ◽  
Partial Differential ◽  
Transform Method ◽  
Initial And Boundary Conditions ◽  
Effects Of Radiation

The effects of radiation and magnetohydrodynamic on unsteady Casson fluid through an accelerated plate is analysed. The problem is formulated in the form of Partial Differential Equations (PDE) with imposed initial and boundary conditions. The Partial Differential Equations are transformed into dimensionless form by introducing suitable non-dimensional variables. Laplace transform method is used to derive the exact solutions for temperature and velocity profiles, fulfilling all initial and boundary conditions. The effects of parameters are depicted and illustrated graphically for radiation, Casson fluid and time, as well as Magnetohydrodynamics (MHD). It is found that the thermal radiation rises due to an increase in temperature. Besides, the increasing of Casson fluid and MHD parameter has decreasing effect on velocity. Finally, the influence of time will increase the velocity of the fluid.

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.

scholarly journals Double Laplace Transform Method for Solving Space and Time Fractional Telegraph Equations

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Ranjit R. Dhunde ◽  
G. L. Waghmare
Keyword(s):  
Boundary Conditions ◽  
Laplace Transform ◽  
Exact Solutions ◽  
Space Time ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Space And Time ◽  
Double Laplace Transform ◽  
Telegraph Equations ◽  
Initial And Boundary Conditions

Double Laplace transform method is applied to find exact solutions of linear/nonlinear space-time fractional telegraph equations in terms of Mittag-Leffler functions subject to initial and boundary conditions. Furthermore, we give illustrative examples to demonstrate the efficiency of the method.

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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