Abstract
The goal of this paper is to investigate existence of solutions for the multiterm nonlinear fractional q-integro-differential {}^{c}D_{q}^{alpha } u(t) in two modes equations and inclusions of order alphain(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.
Highlights
1 Introduction Fractional calculus and q-calculus are the significant branches in mathematical analysis
The field of fractional calculus has countless applications, and the subject of fractional differential equations ranges from the theoretical views of existence and uniqueness of solutions to the analytical and mathematical methods for finding solutions
There has been an intensive development in fractional differential equations and inclusion
Summary
Fractional calculus and q-calculus are the significant branches in mathematical analysis. In 2013, Baleanu, Rezapour and Mohammadi et al, by using fixed-point methods, studied the existence and uniqueness of a solution for the nonlinear fractional differential equation boundary-value problem Dαu(t) = f (t, u(t)) with a Riemann–Liouville fractional derivative via the different boundary-value conditions: u(0) = u(δ), as well as the threepoint boundary condition u(0) = β1u(η) and u(δ) = β2u(η), where δ > 0, t ∈ I = [0, δ], α ∈ (0, 1) η ∈ (0, δ) and 0 < β1 < β2 < 1 [12]. In 2017, Baleanu, Mousalou and Rezapour presented a new method to investigate some fractional integro-differential equations involving the Caputo–Fabrizio derivative.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
