Nonlocal Hadamard fractional integral conditions for nonlinear Riemann-Liouville fractional differential equations

In this paper, we introduce a new class of boundary value problems consisting of a fractional differential equation of Riemann-Liouville type, D q R L x ( t ) = f ( t , x ( t ) ) , t ∈ [ 0 , T ] , subject to the Hadamard fractional integral conditions x ( 0 ) = 0 , x ( T ) = ∑ i = 1 n α i H I p i x...

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Published inBoundary value problems Vol. 2014; no. 1; pp. 1 - 16
Main Authors Tariboon, Jessada, Ntouyas, Sotiris K, Sudsutad, Weerawat
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 09.12.2014
Subjects
Analysis
Approximations and Expansions
Boundary value problems
Difference and Functional Equations
Differential equations
Existence theorems
Integrals
Mathematical analysis
Mathematics
Mathematics and Statistics
Nonlinearity
Ordinary Differential Equations
Partial Differential Equations
Texts
Theorems
Uniqueness
existence
uniqueness
fixed point theorems
Riemann-Liouville fractional derivative
Hadamard fractional integral
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Summary:In this paper, we introduce a new class of boundary value problems consisting of a fractional differential equation of Riemann-Liouville type, D q R L x ( t ) = f ( t , x ( t ) ) , t ∈ [ 0 , T ] , subject to the Hadamard fractional integral conditions x ( 0 ) = 0 , x ( T ) = ∑ i = 1 n α i H I p i x ( η i ) . Existence and uniqueness results are obtained by using a variety of fixed point theorems. Examples illustrating the results obtained are also presented. MSC: 34A08, 34B15.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
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ISSN:1687-2770
1687-2770
DOI:10.1186/s13661-014-0253-9