**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}

^{a}Department of Mathematics, College of Science, University of Duhok, Duhok 42001, IRAQ

^{b}Department 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 *L*_{p}-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, *L*_{p} space

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