|
Title
|
Existence of solutions for equations and inclusions of multi-term fractional $q$-integro-differential with non-separated and initial boundary conditions
|
|
Type
|
JournalPaper
|
|
Keywords
|
Positive solutions; Fractional q-differential inclusions; Fractional q-differential equations; Caputo fractional q-derivative; Riemann-Liouville fractional q-integral
|
|
Abstract
|
The goal of this paper is to investigate existence of solutions for the multi-term nonlinear fractional q-integro-differential ${}^cD_q^{\alpha} u(t)$ in two modes equations and inclusions of order $\alpha \in (n -1, n]$, with non-separated boundary and initial boundary conditions where natural number $n$ is more than or equal to five. We consider Carath\'{e}odory multivalued map and using some fixed point theorems such as Leary-Schauder and Covitz-Nadler famous theorems for finding solutions of the inclusion problems. besides, we present results whenever the multi-functions are convex and non-convex. Lastly, we give some examples illustrating the primary effects.
|
|
Researchers
|
(Third Researcher), Ghorban Khlilzadeh Ranjbar (Second Researcher), Mohammad Esmael Samei (First Researcher)
|