Sign in to use this feature.

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline
remove_circle_outline

Journals

Article Types

Countries / Regions

Search Results (1)

Search Parameters:
Keywords = Gripenberg-type equations

Order results
Result details
Results per page
Select all
Export citation of selected articles as:
18 pages, 337 KB  
Article
Integrable Solutions for Gripenberg-Type Equations with m-Product of Fractional Operators and Applications to Initial Value Problems
by Ateq Alsaadi, Mieczysław Cichoń and Mohamed M. A. Metwali
Mathematics 2022, 10(7), 1172; https://doi.org/10.3390/math10071172 - 4 Apr 2022
Cited by 11 | Viewed by 2060
Abstract
In this paper, we deal with the existence of integrable solutions of Gripenberg-type equations with m-product of fractional operators on a half-line R+=[0,). We prove the existence of solutions in some weighted spaces of [...] Read more.
In this paper, we deal with the existence of integrable solutions of Gripenberg-type equations with m-product of fractional operators on a half-line R+=[0,). We prove the existence of solutions in some weighted spaces of integrable functions, i.e., the so-called L1N-solutions. Because such a space is not a Banach algebra with respect to the pointwise product, we cannot follow the idea of the proof for continuous solutions, and we prefer a fixed point approach concerning the measure of noncompactness to obtain our results. Appropriate measures for this space and some of its subspaces are introduced. We also study the problem of uniqueness of solutions. To achieve our goal, we utilize a generalized Hölder inequality on the noted spaces. Finally, to validate our results, we study the solvability problem for some particularly interesting cases and initial value problems. Full article
(This article belongs to the Special Issue Fractional Differential Equations: Theory and Application)
Back to TopTop