On nonlinear fractional integrodifferential equations with non local condition in Banach spaces

2013 ◽  
Vol 1 ◽  
pp. 129-141 ◽  
Author(s):  
S. D. Kendre ◽  
T. B. Jagtap ◽  
V. V. Kharat
Keyword(s):  
Banach Spaces ◽  
Integrodifferential Equations ◽  
Local Condition ◽  
Non Local

scholarly journals Nonnegative solutions of two-point boundary value problems for nonlinear second order integrodifferential equations in Banach spaces

1991 ◽  
Vol 4 (1) ◽  
pp. 47-69 ◽  
Author(s):  
Dajun Guo
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Theory ◽  
Index Theory ◽  
Point Theory ◽  
Second Order ◽  
Integrodifferential Equations ◽  
Third Order ◽  
Nonnegative Solutions ◽  
Fixed Point Index Theory

In this paper, we combine the fixed point theory, fixed point index theory and cone theory to investigate the nonnegative solutions of two-point BVP for nonlinear second order integrodifferential equations in Banach spaces. As application, we get some results for the third order case. Finally, we give several examples for both infinite and finite systems of ordinary nonlinear integrodifferential equations.

scholarly journals Existence of Fractional Impulsive Functional Integro-Differential Equations in Banach Spaces

2019 ◽  
Vol 2 (2) ◽  
pp. 18 ◽  
Author(s):  
Dimplekumar Chalishajar ◽  
Chokkalingam Ravichandran ◽  
Shanmugam Dhanalakshmi ◽  
Rangasamy Murugesu
Keyword(s):  
Fixed Point ◽  
Group Theory ◽  
Differential Equations ◽  
Banach Spaces ◽  
Fractional Order ◽  
Fixed Point Theorems ◽  
Mild Solutions ◽  
Order System ◽  
Semi Group ◽  
Non Local

In this paper, we establish the existence of piece wise (PC)-mild solutions (defined in Section 2) for non local fractional impulsive functional integro-differential equations with finite delay. The proofs are obtained using techniques of fixed point theorems, semi-group theory and generalized Bellman inequality. In this paper, we used the distributed characteristic operators to define a mild solution of the system. We also discussed the controversy related to the solution operator for the fractional order system using weak and strong Caputo derivatives. Examples are given to illustrate the theory.

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