Nonlocal Fractional Boundary Value Problems Involving Mixed Right and Left Fractional Derivatives and Integrals

被引：4

作者：

Alsaedi, Ahmed ^{[1
]}

Broom, Abrar ^{[1
]}

Ntouyas, Sotiris K. ^{[1
,2
]}

Ahmad, Bashir ^{[1
]}

机构：

[1] King Abdulaziz Univ, Fac Sci, Dept Math, Nonlinear Anal & Appl Math NAAM Res Grp, POB 80203, Jeddah 21589, Saudi Arabia

[2] Univ Ioannina, Dept Math, Ioannina 45110, Greece

来源：

AXIOMS | 2020年 / 9卷 / 02期

关键词：

fractional differential equations; fractional differential inclusions; existence; fixed point theorems; DIFFERENTIAL-EQUATIONS; INCLUSIONS; CONTROLLABILITY; EXISTENCE; SYSTEMS; CAPUTO; SET;

D O I：

10.3390/axioms9020050

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the existence of solutions for nonlocal single and multi-valued boundary value problems involving right-Caputo and left-Riemann-Liouville fractional derivatives of different orders and right-left Riemann-Liouville fractional integrals. The existence of solutions for the single-valued case relies on Sadovskii's fixed point theorem. The first existence results for the multi-valued case are proved by applying Bohnenblust-Karlin's fixed point theorem, while the second one is based on Martelli's fixed point theorem. We also demonstrate the applications of the obtained results.

引用

页数：16

共 50 条

[21] Higher order fractional boundary value problems for mixed type derivatives
Khaldi, Rabah
Guezane-Lakoud, Assia
Journal of Nonlinear Functional Analysis, 2017, 2017
[22] On the mixed fractional quantum and Hadamard derivatives for impulsive boundary value problems
Niyoom, Somboon
Ntouyas, Sotiris K.
Sudprasert, Chayapat
Tariboon, Jessada
OPEN MATHEMATICS, 2021, 19 (01): : 1598 - 1611
[23] Fractional order differential systems involving right Caputo and left Riemann–Liouville fractional derivatives with nonlocal coupled conditions
Bashir Ahmad
Sotiris K. Ntouyas
Ahmed Alsaedi
Boundary Value Problems, 2019
[24] Recent studies on boundary value problems for impulsive fractional differential systems involving Caputo fractional derivatives
Liu Y.
Wong P.J.Y.
Boletín de la Sociedad Matemática Mexicana, 2018, 24 (2) : 393 - 425
[25] NONLOCAL BOUNDARY VALUE PROBLEMS FOR FRACTIONAL DIFFERENTIAL EQUATIONS
Stanek, Svatoslav
MEMOIRS ON DIFFERENTIAL EQUATIONS AND MATHEMATICAL PHYSICS, 2011, 54 : 99 - 115
[26] On impulsive nonlocal integro-initial value problems involving multi-order Caputo-type generalized fractional derivatives and generalized fractional integrals
Ahmad, Bashir
Alghanmi, Madeaha
Nieto, Juan J.
Alsaedi, Ahmed
ADVANCES IN DIFFERENCE EQUATIONS, 2019, 2019 (1)
[27] On impulsive nonlocal integro-initial value problems involving multi-order Caputo-type generalized fractional derivatives and generalized fractional integrals
Bashir Ahmad
Madeaha Alghanmi
Juan J. Nieto
Ahmed Alsaedi
Advances in Difference Equations, 2019
[28] On a class of sequential fractional q-integrodifference boundary value problems involving different numbers of q in derivatives and integrals
Patanarapeelert, Nichaphat
Sriphanomwan, Umaporn
Sitthiwirattham, Thanin
ADVANCES IN DIFFERENCE EQUATIONS, 2016, : 1 - 16
[29] Eigenvalue problems for fractional differential equations with right and left fractional derivatives
Li, Jing
Qi, Jiangang
APPLIED MATHEMATICS AND COMPUTATION, 2015, 256 : 1 - 10
[30] On a class of sequential fractional q-integrodifference boundary value problems involving different numbers of q in derivatives and integrals
Nichaphat Patanarapeelert
Umaporn Sriphanomwan
Thanin Sitthiwirattham
Advances in Difference Equations, 2016

← 1 2 3 4 5 →