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Volume 34, Issue 3
Existence of Solutions for Fractional Differential Equations Involving Two Riemann-Liouville Fractional Orders

Mohamed Houas

DOI: 10.4208/ata.OA-2017-0021

Anal. Theory Appl., 34 (2018), pp. 253-274.

Published online: 2018-11

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  • Abstract

In this work, we study existence and uniqueness of solutions for multi-point boundary value problem of nonlinear fractional differential equations with two fractional derivatives. By using the variety of fixed point theorems, such as Banach’s fixed point theorem, Leray-Schauder’s nonlinear alternative and Leray-Schauder’s degree theory, the existence of solutions is obtained. At the end, some illustrative examples are discussed.

  • Keywords

Riemann-Liouville integral, existence, fixed point theorem, Leray-Schauder alternative.

  • AMS Subject Headings

26A33, 34A12, 34A08

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-34-253, author = {Mohamed Houas}, title = {Existence of Solutions for Fractional Differential Equations Involving Two Riemann-Liouville Fractional Orders}, journal = {Analysis in Theory and Applications}, year = {2018}, volume = {34}, number = {3}, pages = {253--274}, abstract = {

In this work, we study existence and uniqueness of solutions for multi-point boundary value problem of nonlinear fractional differential equations with two fractional derivatives. By using the variety of fixed point theorems, such as Banach’s fixed point theorem, Leray-Schauder’s nonlinear alternative and Leray-Schauder’s degree theory, the existence of solutions is obtained. At the end, some illustrative examples are discussed.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-2017-0021}, url = {http://global-sci.org/intro/article_detail/ata/12840.html} }
TY - JOUR T1 - Existence of Solutions for Fractional Differential Equations Involving Two Riemann-Liouville Fractional Orders AU - Mohamed Houas JO - Analysis in Theory and Applications VL - 3 SP - 253 EP - 274 PY - 2018 DA - 2018/11 SN - 34 DO - http://doi.org/10.4208/ata.OA-2017-0021 UR - https://global-sci.org/intro/article_detail/ata/12840.html KW - Riemann-Liouville integral, existence, fixed point theorem, Leray-Schauder alternative. AB -

In this work, we study existence and uniqueness of solutions for multi-point boundary value problem of nonlinear fractional differential equations with two fractional derivatives. By using the variety of fixed point theorems, such as Banach’s fixed point theorem, Leray-Schauder’s nonlinear alternative and Leray-Schauder’s degree theory, the existence of solutions is obtained. At the end, some illustrative examples are discussed.

Mohamed Houas. (2018). Existence of Solutions for Fractional Differential Equations Involving Two Riemann-Liouville Fractional Orders. Analysis in Theory and Applications. 34 (3). 253-274. doi:10.4208/ata.OA-2017-0021
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