(k,ψ)-Hilfer Nonlocal Integro-Multi-Point Boundary Value Problems for Fractional Differential Equations and Inclusions
Mathematics
; 10(15):2615, 2022.
Article
in English
| ProQuest Central | ID: covidwho-1994103
ABSTRACT
In this paper, we establish existence and uniqueness results for single-valued as well as multi-valued (k,ψ)-Hilfer boundary value problems of order in (1,2], subject to nonlocal integro-multi-point boundary conditions. In the single-valued case, we use Banach and Krasnosel’skiĭ fixed point theorems as well as a Leray–Schauder nonlinear alternative to derive the existence and uniqueness results. For the multi-valued problem, we prove two existence results for the convex and non-convex nature of the multi-valued map involved in a problem by applying a Leray–Schauder nonlinear alternative for multi-valued maps, and a Covitz–Nadler fixed point theorem for multi-valued contractions, respectively. Numerical examples are presented for illustration of all the obtained results.
Mathematics; (k,ψ)-Hilfer fractional derivative; Riemann–Liouville fractional derivative; Caputo fractional derivative; existence; uniqueness; fixed point theorems; Boundary conditions; Inclusions; Theorems; Fractional calculus; Differential equations; Maps; Coronaviruses; Boundary value problems; Fixed points (mathematics); COVID-19
Full text:
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Collection:
Databases of international organizations
Database:
ProQuest Central
Language:
English
Journal:
Mathematics
Year:
2022
Document Type:
Article
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