Existence of solutions for equations and inclusions of multiterm fractional q-integro-differential with nonseparated and initial boundary conditions

• Main Authors: Mohammad Esmael Samei, Ghorban Khalilzadeh Ranjbar, Vahid Hedayati
• Format: Article
• Language: English
• Published: SpringerOpen 2019-10-01
• Series: Journal of Inequalities and Applications
• Subjects: Positive solutions; Fractional q-differential inclusions; Fractional q-differential equations; Caputo fractional q-derivative; Riemann–Liouville fractional q-integral
• Online Access: http://link.springer.com/article/10.1186/s13660-019-2224-2

Abstract The goal of this paper is to investigate existence of solutions for the multiterm nonlinear fractional q-integro-differential Dqαcu(t) ${}^{c}D_{q}^{\alpha } u(t)$ in two modes equations and inclusions of order α∈(n−1,n] $\alpha\in(n -1, n]$, with non-separated boundary and initial boundary conditions where the natural number n is more than or equal to five. We consider a Carathéodory multivalued map and use Leray–Schauder and Covitz–Nadler famous fixed point theorems for finding solutions of the inclusion problems. Besides, we present results whenever the multifunctions are convex and nonconvex. Lastly, we give some examples illustrating the primary effects.