Nonlinear Caputo fractional derivative with nonlocal Riemann-Liouville fractional integral condition via fixed point theorems

Journal article

Authors/Editors

POOM KUMAM

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Publication Details

Author list: Borisut P., Kumam P., Ahmed I., Sitthithakerngkiet K.

Publisher: MDPI AG

Publication year: 2019

Volume number: 11

Issue number: 6

ISSN: 2073-8994

eISSN: 2073-8994

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85068087509&doi=10.3390%2fsym11060829&partnerID=40&md5=eb24438dee6a2a1e23b2ba0ff7983369

Languages: English-Great Britain (EN-GB)

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Abstract

In this paper, we study and investigate an interesting Caputo fractional derivative and Riemann-Liouville integral boundary value problem (BVP):where n - 1 < q < n, n ≥ 2, m, n ∈ N, ζk, βi ∈ ℝ, k = 0, 1, . . ., n -2, i = 1, 2, . . ., m, and cDq 0+ is the Caputo fractional derivatives, f: [0, T] × C([0, T], E) &p.→ E, where E is the Banach space. The space E is chosen as an arbitrary Banach space; it can also be ℝ (with the absolute value) or C([0, T],ℝ) with the supremum-norm. RL I pi0+ is the Riemann-Liouville fractional integral of order pi > 0, hi 2 (0, T) Via the fixed point theorems of Krasnoselskii and Darbo, the authors study the existence of solutions to this problem. An example is included to illustrate the applicability of their results. © 2019 by the authors.

Keywords

Existence of a solution, Integral boundary value problems