Regular fractional differential equations in the Sobolev space

2017 ◽  
Vol 20 (3) ◽  
Author(s):  
Ekin Ugurlu ◽  
Dumitru Baleanu ◽  
Kenan Tas
Keyword(s):  
Sobolev Space ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Fractional Differential Equations ◽  
Symmetric Operator ◽  
Boundary Value ◽  
Inner Products ◽  
Sturm Liouville ◽  
Fractional Differential

AbstractIn this paper regular fractional Sturm-Liouville boundary value problems are considered. In particular, new inner products are described in the Sobolev space and a symmetric operator is established in this space.

scholarly journals A numerical scheme for problems in fractional calculus

2018 ◽  
Vol 20 ◽  
pp. 02001
Author(s):  
M. Razzaghi
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Fractional Differential Equations ◽  
Numerical Scheme ◽  
Boundary Value ◽  
Bernoulli Polynomials ◽  
Algebraic Equations ◽  
Hybrid Functions ◽  
Block Pulse Functions ◽  
Fractional Differential

In this paper, a new numerical method for solving the fractional differential equations with boundary value problems is presented. The method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The Riemann-Liouville fractional integral operator for hybrid functions is given. This operator is then utilized to reduce the solution of the boundary value problems for fractional differential equations to a system of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.

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