Results on controllability of Hilfer fractional differential equations with infinite delay via measures of noncompactness

2021 ◽  
Author(s):  
K. Kavitha ◽  
V. Vijayakumar ◽  
R. Udhayakumar ◽  
C. Ravichandran
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Infinite Delay ◽  
Measures Of Noncompactness ◽  
Fractional Differential

scholarly journals Applications of measures of noncompactness to infinite system of fractional differential equations

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3421-3432 ◽  
Author(s):  
Mohammad Mursaleen ◽  
Bilal Bilalov ◽  
Syed Rizvi
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence Result ◽  
Measure Of Noncompactness ◽  
Infinite System ◽  
Hausdorff Measure Of Noncompactness ◽  
Measures Of Noncompactness ◽  
Banach Sequence Spaces ◽  
Fractional Differential ◽  
Banach Sequence

In this paper, we discuss few existence result for solution of an infinite system of fractional differential equations of order ?(1 < ? < 2), with three point boundary value problem in the interval [0, T]. The problem is studied in the classical Banach sequence spaces c0 and lp (1 ? p < 1), using Hausdorff measure of noncompactness and Darbo type fixed point theorem. We also illustrate our results through some concrete examples.

Solvability for a couple system of nonlinear fractional differential equations in a Banach space

2013 ◽  
Vol 16 (1) ◽  
Author(s):  
Jitai Liang ◽  
Zhenhai Liu ◽  
Xuhuan Wang
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Couple System ◽  
Measures Of Noncompactness ◽  
Nonlinear Fractional Differential Equations ◽  
Fractional Differential ◽  
The Fixed Point Theorem

AbstractIn this paper, we study boundary value problems of nonlinear fractional differential equations in a Banach Space E of the following form: $\left\{ \begin{gathered} D_{0^ + }^p x(t) = f_1 (t,x(t),y(t)),t \in J = [0,1], \hfill \\ D_{0^ + }^q y(t) = f_2 (t,x(t),y(t)),t \in J = [0,1], \hfill \\ x(0) + \lambda _1 x(1) = g_1 (x,y), \hfill \\ y(0) + \lambda _2 y(1) = g_2 (x,y), \hfill \\ \end{gathered} \right. $ where D 0+ denotes the Caputo fractional derivative, 0 < p,q ≤ 1. Some new results on the solutions are obtained, by the concept of measures of noncompactness and the fixed point theorem of Mönch type.

scholarly journals Weighted fractional differential equations with infinite delay in Banach spaces

2016 ◽  
Vol 14 (1) ◽  
pp. 370-383 ◽  
Author(s):  
Qixiang Dong ◽  
Can Liu ◽  
Zhenbin Fan
Keyword(s):  
Differential Equations ◽  
Banach Spaces ◽  
Fractional Differential Equations ◽  
Fractional Derivatives ◽  
Fixed Point Theorems ◽  
Infinite Delay ◽  
Type Inequality ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential

AbstractThis paper is devoted to the study of fractional differential equations with Riemann-Liouville fractional derivatives and infinite delay in Banach spaces. The weighted delay is developed to deal with the case of non-zero initial value, which leads to the unboundedness of the solutions. Existence and uniqueness results are obtained based on the theory of measure of non-compactness, Schaude’s and Banach’s fixed point theorems. As auxiliary results, a fractional Gronwall type inequality is proved, and the comparison property of fractional integral is discussed.

scholarly journals Boundary Value Problems for Hybrid Caputo Fractional Differential Equations

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 282 ◽  
Author(s):  
Zidane Baitiche ◽  
Kaddour Guerbati ◽  
Mouffak Benchohra ◽  
Yong Zhou
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Fractional Differential Equations ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Main Tool ◽  
Measures Of Noncompactness ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential

In this paper, we discuss the existence of solutions for a hybrid boundary value problem of Caputo fractional differential equations. The main tool used in our study is associated with the technique of measures of noncompactness. As an application, we give an example to illustrate our results.

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