scholarly journals Existence of Solutions to Fractional Mixed Integrodifferential Equations with Nonlocal Initial Condition

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
A. Anguraj ◽  
P. Karthikeyan ◽  
J. J. Trujillo
Keyword(s):  
Existence Of Solutions ◽  
Integrodifferential Equations ◽  
Initial Condition ◽  
Nonlocal Initial Condition

scholarly journals Existence of solutions for impulsive fractional integrodifferential equations involving Gronwall’s inequality in Banach spaces

2012 ◽  
Vol 21 (2) ◽  
pp. 115-122
Author(s):  
A. AL-OMARI ◽  
◽  
M. H. M. RASHID ◽  
K. KARTHIKEYAN ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fractional Calculus ◽  
Banach Spaces ◽  
Caputo Derivative ◽  
Existence Of Solutions ◽  
Sufficient Conditions ◽  
Fixed Point Method ◽  
Integrodifferential Equations ◽  
Gronwall’S Inequality ◽  
Mild Conditions

In this paper, we study boundary value problems for impulsive fractional integrodifferential equations involving Caputo derivative in Banach spaces. A generalized singular type Gronwall inequality is given to obtain an important priori bounds. Some sufficient conditions for the existence solutions are established by virtue of fractional calculus and fixed point method under some mild conditions.

scholarly journals A Nonlinear Fractional Problem with Mixed Volterra-Fredholm Integro-Differential Equation: Existence, Uniqueness, H-U-R Stability, and Regularity of Solutions

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Somia Khaldi ◽  
Rachid Mecheraoui ◽  
Aiman Mukheimer
Keyword(s):  
Differential Equation ◽  
Functional Derivative ◽  
Regularity Of Solutions ◽  
Initial Condition ◽  
Stability Of Solutions ◽  
Nonlocal Initial Condition ◽  
Integro Differential Equation ◽  
Fixed Point Approach ◽  
Pantograph Equation ◽  
Rassias Stability

This paper considers nonlinear fractional mixed Volterra-Fredholm integro-differential equation with a nonlocal initial condition. We propose a fixed-point approach to investigate the existence, uniqueness, and Hyers-Ulam-Rassias stability of solutions. Results of this paper are based on nonstandard assumptions and hypothesis and provide a supplementary result concerning the regularity of solutions. We show and illustrate the wide validity field of our findings by an example of problem with nonlocal neutral pantograph equation, involving functional derivative and ψ -Caputo fractional derivative.

scholarly journals Existence of Solutions of a Class of Abstract Second Order Nonlinear Integrodifferential Equations

2002 ◽  
Vol 15 (2) ◽  
pp. 115-124 ◽  
Author(s):  
K. Balachandran ◽  
J. Y. Park
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Second Order ◽  
Integrodifferential Equations ◽  
Cosine Families ◽  
Schaefer Fixed Point Theorem ◽  
Families Of Operators

In this paper we prove the existence of solutions of nonlinear second order integrodifferential equations in Banach spaces. The results are obtained by using the theory of strongly continuous cosine families of operators and the Schaefer fixed point theorem.

scholarly journals Existence of solutions and controllability of nonlinear integrodifferential systems in Banach spaces

2003 ◽  
Vol 2003 (2) ◽  
pp. 65-79 ◽  
Author(s):  
K. Balachandran ◽  
J. Y. Park
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Strong Solutions ◽  
Integrodifferential Equations ◽  
Schäuder Fixed Point Theorem

We prove the existence of mild and strong solutions of integrodifferential equations with nonlocal conditions in Banach spaces. Further sufficient conditions for the controllability of integrodifferential systems are established. The results are obtained by using the Schauder fixed-point theorem. Examples are provided to illustrate the theory.

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