Solvability of Gripenberg's equations of fractional order with perturbation term in weighted $L_p$-spaces on ${\mathbb{R}}^+$

Authors

MOHAMED M. A. METWALI

DOI

10.3906/mat-2106-84

Abstract

This article deals with the solvability of Gripenberg's equations of fractional order with a perturbation term in weighted Lebesgue spaces on ${\mathbb{R}}^+=[0,\infty)$ via the fixed point hypothesis and the measure of noncompactness. The uniqueness of the solutions for the studied problem is discussed. An example is included to validate our results. The results presented in the article extend and generalize some former results in the available literature.

Keywords

Measure of noncompactness, Gripenberg's equations, fractional calculus, weighted Lebesgue spaces, Schauder fixed point theorem

First Page

481

Last Page

498

Recommended Citation

METWALI, MOHAMED M. A. (2022) "Solvability of Gripenberg's equations of fractional order with perturbation term in weighted $L_p$-spaces on ${\mathbb{R}}^+$," Turkish Journal of Mathematics: Vol. 46: No. 2, Article 11. https://doi.org/10.3906/mat-2106-84
Available at: https://journals.tubitak.gov.tr/math/vol46/iss2/11