On More General Fractional Differential Equations Involving Mixed Generalized Derivatives with Nonlocal Multipoint and Generalized Fractional Integral Boundary Conditions

This paper deals with the existence of solutions for a new boundary value problem involving mixed generalized fractional derivatives of Riemann-Liouville and Caputo supplemented with nonlocal multipoint boundary conditions. The existence results for inclusion case are also discussed. The nonlinear t...

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Bibliographic Details
Published in:Journal of function spaces 2020, Vol.2020 (2020), p.1-19
Main Authors: Shammakh, Wafa, AlQahtani, Bushra A., Alzumi, Hadeel Z.
Format: Article
Language:English
Subjects:
Banach spaces
Boundary conditions
Boundary value problems
Calculus
Derivatives
Differential equations
Fixed points (mathematics)
Integral equations
Integrals
Mathematical functions
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Summary:This paper deals with the existence of solutions for a new boundary value problem involving mixed generalized fractional derivatives of Riemann-Liouville and Caputo supplemented with nonlocal multipoint boundary conditions. The existence results for inclusion case are also discussed. The nonlinear term belongs to a general abstract space, and our results rely on modern theorems of fixed point. Ulam stability is also presented. We provide some examples that well-illustrate our main results.
ISSN:2314-8896
2314-8888
DOI:10.1155/2020/3102142