scholarly journals On the existence and stability for noninstantaneous impulsive fractional integrodifferential equation

2018 ◽  
Vol 42 (4) ◽  
pp. 1249-1261 ◽  
Author(s):  
José Vanterler da Costa Sousa ◽  
Daniela dos Santos Oliveira ◽  
Edmundo Capelas de Oliveira
Keyword(s):  
Integrodifferential Equation ◽  
Existence And Stability ◽  
Fractional Integrodifferential Equation

scholarly journals Existence Results for an Impulsive Neutral Fractional Integrodifferential Equation with Infinite Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Alka Chadha ◽  
Dwijendra N. Pandey
Keyword(s):  
Banach Space ◽  
Mild Solution ◽  
Hausdorff Measure ◽  
Integrodifferential Equation ◽  
Measure Of Noncompactness ◽  
Infinite Delay ◽  
Existence Results ◽  
Hausdorff Measure Of Noncompactness ◽  
Arbitrary Banach Space ◽  
Fractional Integrodifferential Equation

We consider an impulsive neutral fractional integrodifferential equation with infinite delay in an arbitrary Banach spaceX. The existence of mild solution is established by using solution operator and Hausdorff measure of noncompactness.

scholarly journals Solving Fuzzy Volterra Integrodifferential Equations of Fractional Order by Bernoulli Wavelet Method

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
R. Mastani Shabestari ◽  
R. Ezzati ◽  
T. Allahviranloo
Keyword(s):  
Integrodifferential Equation ◽  
Matrix Equation ◽  
Matrix Method ◽  
Integrodifferential Equations ◽  
Algebraic Equations ◽  
Wavelet Method ◽  
Collocation Points ◽  
Nonlinear Algebraic Equations ◽  
Bernoulli Wavelet ◽  
Fractional Integrodifferential Equation

A matrix method called the Bernoulli wavelet method is presented for numerically solving the fuzzy fractional integrodifferential equations. Using the collocation points, this method transforms the fuzzy fractional integrodifferential equation to a matrix equation which corresponds to a system of nonlinear algebraic equations with unknown coefficients. To illustrate the method, it is applied to certain fuzzy fractional integrodifferential equations, and the results are compared.

scholarly journals On a Time-Fractional Integrodifferential Equation via Three-Point Boundary Value Conditions

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Dumitru Baleanu ◽  
Shahram Rezapour ◽  
Sina Etemad ◽  
Ahmed Alsaedi
Keyword(s):  
Fractional Differential Equations ◽  
Integrodifferential Equation ◽  
Numerical Solutions ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Uniqueness Theorems ◽  
Point Boundary ◽  
Real World Applications ◽  
Fractional Differential ◽  
Fractional Integrodifferential Equation

The existence and the uniqueness theorems play a crucial role prior to finding the numerical solutions of the fractional differential equations describing the models corresponding to the real world applications. In this paper, we study the existence of solutions for a time-fractional integrodifferential equation via three-point boundary value conditions.

Controllability for some nonlinear impulsive partial functional integrodifferential systems with infinite delay in Banach spaces

2020 ◽  
Vol 4 (2) ◽  
pp. 104-115
Author(s):  
Khalil Ezzinbi ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Integrodifferential Equation ◽  
Resolvent Operator ◽  
Measure Of Noncompactness ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Mönch Fixed Point Theorem ◽  
The Resolvent Operator

This work concerns the study of the controllability for some impulsive partial functional integrodifferential equation with infinite delay in Banach spaces. We give sufficient conditions that ensure the controllability of the system by supposing that its undelayed part admits a resolvent operator in the sense of Grimmer, and by making use of the measure of noncompactness and the Mönch fixed-point Theorem. As a result, we obtain a generalization of the work of K. Balachandran and R. Sakthivel (Journal of Mathematical Analysis and Applications, 255, 447-457, (2001)) and a host of important results in the literature, without assuming the compactness of the resolvent operator. An example is given for illustration.

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