Article ID: MTJPAM-D-21-00050

Title: p-integrable solution of boundary fractional differential and integro-differential equations with Riemann derivatives of order (n − 1 < δ ≤ n)


Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-21-00050; Volume 4 / Issue 2 / Year 2022, Pages 1-10

Document Type: Research Paper

Author(s): Dilsher N. Abdulqader a , Shayma Adil Murad b

aDepartment of Mathematics, College of Science, University of Duhok, Duhok 42001, IRAQ

bDepartment of Mathematics, College of Science, University of Duhok, Duhok 42001, IRAQ

Received: 25 July 2021, Accepted: 9 March 2022, Published: 12 April 2022.

Corresponding Author: Shayma Adil Murad (Email address: shaymaadil@uod.ac)

Full Text: PDF

Abstract

This paper considers the existence of Lp-solutions of certain fractional differential and integro-differential equations involving the Riemann derivatives of order (n − 1 < δ ≤ n), with boundary conditions. The results are established by means of the Hölder’s inequality in a Banach space. Some special cases and examples are given to explain the main results.

Keywords: Fracional differential equations, integro-differential equations, Riemann fractional derivatives, existence and uniqueness, Hölder’s inequality, Lp space

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