scholarly journals The existence and uniqueness of mild solutions for fractional differential equations with nonlocal conditions of order 1<α<2

2012 ◽  
Vol 64 (6) ◽  
pp. 2100-2110 ◽  
Author(s):  
Xiao-Bao Shu ◽  
Qianqian Wang
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Mild Solutions ◽  
Nonlocal Conditions ◽  
Fractional Differential

scholarly journals Existence and uniqueness results for nonlinear implicit Riemann-Liouville fractional differential equations with nonlocal conditions

Filomat ◽  
2020 ◽  
Vol 34 (14) ◽  
pp. 4881-4891
Author(s):  
Adel Lachouri ◽  
Abdelouaheb Ardjouni ◽  
Ahcene Djoudi
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theory ◽  
Nonlocal Conditions ◽  
Point Theory ◽  
Uniqueness Of Solutions ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential

In this paper, we use the fixed point theory to obtain the existence and uniqueness of solutions for nonlinear implicit Riemann-Liouville fractional differential equations with nonlocal conditions. An example is given to illustrate this work.

scholarly journals Existence of the Solution for System of Coupled Hybrid Differential Equations with Fractional Order and Nonlocal Conditions

2016 ◽  
Vol 2016 ◽  
pp. 1-9
Author(s):  
Khalid Hilal ◽  
Ahmed Kajouni
Keyword(s):  
Differential Equations ◽  
Existence Theorem ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Differential Operators ◽  
Nonlocal Conditions ◽  
Uniqueness Result ◽  
Carathéodory Conditions ◽  
Fractional Differential ◽  
Hybrid Differential Equations

This paper is motivated by some papers treating the fractional hybrid differential equations with nonlocal conditions and the system of coupled hybrid fractional differential equations; an existence theorem for fractional hybrid differential equations involving Caputo differential operators of order1<α≤2is proved under mixed Lipschitz and Carathéodory conditions. The existence and uniqueness result is elaborated for the system of coupled hybrid fractional differential equations.

Existence results for semilinear fractional differential equations via Kuratowski measure of noncompactness

2012 ◽  
Vol 15 (4) ◽  
Author(s):  
Kexue Li ◽  
Jigen Peng ◽  
Jinghuai Gao
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Measure Of Noncompactness ◽  
Fixed Point Theory ◽  
Mild Solutions ◽  
Nonlocal Conditions ◽  
Point Theory ◽  
Kuratowski Measure Of Noncompactness ◽  
Condensing Operator ◽  
Fractional Differential

AbstractIn this paper, we study the existence of mild solutions for a class of semilinear fractional differential equations with nonlocal conditions in Banach spaces. The results are obtained by using convex-power condensing operator and fixed point theory. An example is presented to illustrate the main result.

scholarly journals Existence and Stability Analysis for Fractional Differential Equations with Mixed Nonlocal Conditions

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 117 ◽  
Author(s):  
Suphawat Asawasamrit ◽  
Woraphak Nithiarayaphaks ◽  
Sotiris Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Nonlocal Conditions ◽  
Ulam Stability ◽  
Existence And Stability ◽  
Fractional Differential ◽  
Mixed Fractional Derivatives

In this paper, we study the existence and uniqueness of solution for fractional differential equations with mixed fractional derivatives, integrals and multi-point conditions. After that, we also establish different kinds of Ulam stability for the problem at hand. Examples illustrating our results are also presented.

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