New class of boundary value problem for nonlinear fractional differential equations involving Erdélyi-Kober derivative

Yacine Arioua; Maria Titraoui

Communications in Mathematics (2019)

  • Volume: 27, Issue: 2, page 113-141
  • ISSN: 1804-1388

Abstract

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In this paper, we introduce a new class of boundary value problem for nonlinear fractional differential equations involving the Erdélyi-Kober differential operator on an infinite interval. Existence and uniqueness results for a positive solution of the given problem are obtained by using the Banach contraction principle, the Leray-Schauder nonlinear alternative, and Guo-Krasnosel'skii fixed point theorem in a special Banach space. To that end, some examples are presented to illustrate the usefulness of our main results.

How to cite

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Arioua, Yacine, and Titraoui, Maria. "New class of boundary value problem for nonlinear fractional differential equations involving Erdélyi-Kober derivative." Communications in Mathematics 27.2 (2019): 113-141. <http://eudml.org/doc/295026>.

@article{Arioua2019,
abstract = {In this paper, we introduce a new class of boundary value problem for nonlinear fractional differential equations involving the Erdélyi-Kober differential operator on an infinite interval. Existence and uniqueness results for a positive solution of the given problem are obtained by using the Banach contraction principle, the Leray-Schauder nonlinear alternative, and Guo-Krasnosel'skii fixed point theorem in a special Banach space. To that end, some examples are presented to illustrate the usefulness of our main results.},
author = {Arioua, Yacine, Titraoui, Maria},
journal = {Communications in Mathematics},
keywords = {Fractional differential equations; Boundary value problems; Erdélyi-Kober derivative; Fixed point theorems; Existence; Uniqueness},
language = {eng},
number = {2},
pages = {113-141},
publisher = {University of Ostrava},
title = {New class of boundary value problem for nonlinear fractional differential equations involving Erdélyi-Kober derivative},
url = {http://eudml.org/doc/295026},
volume = {27},
year = {2019},
}

TY - JOUR
AU - Arioua, Yacine
AU - Titraoui, Maria
TI - New class of boundary value problem for nonlinear fractional differential equations involving Erdélyi-Kober derivative
JO - Communications in Mathematics
PY - 2019
PB - University of Ostrava
VL - 27
IS - 2
SP - 113
EP - 141
AB - In this paper, we introduce a new class of boundary value problem for nonlinear fractional differential equations involving the Erdélyi-Kober differential operator on an infinite interval. Existence and uniqueness results for a positive solution of the given problem are obtained by using the Banach contraction principle, the Leray-Schauder nonlinear alternative, and Guo-Krasnosel'skii fixed point theorem in a special Banach space. To that end, some examples are presented to illustrate the usefulness of our main results.
LA - eng
KW - Fractional differential equations; Boundary value problems; Erdélyi-Kober derivative; Fixed point theorems; Existence; Uniqueness
UR - http://eudml.org/doc/295026
ER -

References

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