scholarly journals A Chebyshev spectral method based on operational matrix for initial and boundary value problems of fractional order

2011 ◽  
Vol 62 (5) ◽  
pp. 2364-2373 ◽  
Author(s):  
E.H. Doha ◽  
A.H. Bhrawy ◽  
S.S. Ezz-Eldien
Keyword(s):  
Boundary Value Problems ◽  
Spectral Method ◽  
Fractional Order ◽  
Boundary Value ◽  
Operational Matrix ◽  
Chebyshev Spectral Method

scholarly journals Boundary-value problems for differential equations of fractional order

2013 ◽  
Vol 194 (5) ◽  
pp. 499-512 ◽  
Author(s):  
Temirkhan Sultanovich Aleroev ◽  
Mokhtar Kirane ◽  
Yi-Fa Tang
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Fractional Order ◽  
Boundary Value

Chebyshev spectral method for solving a class of local and nonlocal elliptic boundary value problems

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Harendra Singh
Keyword(s):  
Boundary Value Problems ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
High Accuracy ◽  
Elliptic Boundary Value Problems ◽  
Strong Nonlinearity ◽  
Elliptic Boundary Value ◽  
Chebyshev Spectral Collocation ◽  
Chebyshev Spectral Method ◽  
Chebyshev Spectral Collocation Method

Abstract This paper deals with a class of Bratu’s type, Troesch’s and nonlocal elliptic boundary value problems. Due to strong nonlinearity and presence of parameter δ, it is very difficult to solve these problems. Here we solve these classes of important equations using the Chebyshev spectral collocation method. We have provided the convergence of the proposed approximate method. The trueness of the method is shown by applying it to some illustrative examples. Results are compared with some known methods to highlight its neglectable error and high accuracy.

scholarly journals On Solutions of Fractional Order Boundary Value Problems with Integral Boundary Conditions in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Hussein A. H. Salem ◽  
Mieczysław Cichoń
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Fractional Order ◽  
Nonlinear Term ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Integral Boundary Conditions ◽  
Point Of View ◽  
Integral Boundary ◽  
Special Cases

The object of this paper is to investigate the existence of a class of solutions for some boundary value problems of fractional order with integral boundary conditions. The considered problems are very interesting and important from an application point of view. They include two, three, multipoint, and nonlocal boundary value problems as special cases. We stress on single and multivalued problems for which the nonlinear term is assumed only to be Pettis integrable and depends on the fractional derivative of an unknown function. Some investigations on fractional Pettis integrability for functions and multifunctions are also presented. An example illustrating the main result is given.

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