Boundary Value Problems for Fractional Differential Equations with Integral and Anti-Periodic Conditions in a Banach Space

2018 ◽  
Vol 4 (2) ◽  
pp. 65-70
Author(s):  
Wafaa Benhamida ◽  
John R. Graef ◽  
Samira Hamani
Keyword(s):  
Banach Space ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Fractional Differential

ANTI-PERIODIC TYPE BOUNDARY VALUE PROBLEMS FOR SINGULAR MULTI-TERM FRACTIONAL DIFFERENTIAL EQUATIONS WITH IMPULSE EFFECTS

2013 ◽  
Vol 24 (06) ◽  
pp. 1350047 ◽  
Author(s):  
YUJI LIU
Keyword(s):  
Banach Space ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Continuous Operator ◽  
Weighted Banach Space ◽  
Fractional Differential ◽  
The Fixed Point Theorem ◽  
Type Boundary

Results on the existence of solutions of anti-periodic type boundary value problems for singular multi-term fractional differential equations with impulse effects are established. We first transform the problem into a hybrid system, then construct a weighted Banach space and a completely continuous operator, and finally, we use the fixed point theorem in the Banach space to prove the main results. An example is given to illustrate the efficiency of the main theorems.

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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