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Existence and uniqueness for ψ‐Hilfer fractional differential equation with nonlocal multi‐point condition.
- Source :
-
Mathematical Methods in the Applied Sciences . Feb2021, Vol. 44 Issue 3, p2506-2520. 15p. - Publication Year :
- 2021
-
Abstract
- In this paper, we study and investigate the ψ−Hilfer fractional differential equation with nonlocal multi‐point condition of the form: Da+q,p;ψu(t)=f(t,u(t),Da+q,p;ψu(t)),t∈[a,b],Ia+1−r;ψu(a)=∑i=1mβiu(ηi),q≤r=q+p−qp<1,ηi∈[a,b], where 0<q<1,0≤p≤1,m∈N, βi∈R, i=1,2,...,m, −∞<a<b<∞, Da+q,p;ψ is the ψ− Hilfer fractional derivative, f:[a,b]×R×R→R is a continuous function, and Ia+1−r;ψ is the ψ‐Riemann‐Liouville fractional integral of order 1−r. By using Schaefer's and Banach fixed point theorems, we prove the existence, uniqueness, and stability analysis of this problem. An example is given to illustrate the applicability of our results. [ABSTRACT FROM AUTHOR]
- Subjects :
- *FRACTIONAL differential equations
*FRACTIONAL integrals
*LAPLACIAN operator
Subjects
Details
- Language :
- English
- ISSN :
- 01704214
- Volume :
- 44
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Mathematical Methods in the Applied Sciences
- Publication Type :
- Academic Journal
- Accession number :
- 147923896
- Full Text :
- https://doi.org/10.1002/mma.6092