Existence and stability results of relaxation fractional differential equations with Hilfer-Katugampola fractional derivative

Existence and stability results of relaxation fractional differential equations with Hilfer-Katugampola fractional derivative

In this work, we present the existence, uniqueness, and stability result of solution to the nonlinear fractional differential equations involving Hilfer-Katugampola derivative subject to nonlocal fractional integral boundary conditions. The reasoning is mainly based upon properties of Mittag-Leffle...

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Main Authors: Mohammed. A. Almalahi, Satish. K. Panchal
Format: Article
Language:English
Published: ATNAA 2020-10-01
Series:Advances in the Theory of Nonlinear Analysis and its Applications
Subjects:
hilfer > katugampola fractional derivative
existence
mittag-leffler functions
ulam stability
Online Access:https://dergipark.org.tr/tr/download/article-file/961784
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spelling doaj-cd76d1d04f764bd187e84ea3c6459e1b2020-12-09T07:44:58ZengATNAAAdvances in the Theory of Nonlinear Analysis and its Applications2587-26482587-26482020-10-014429931510.31197/atnaa.686693Existence and stability results of relaxation fractional differential equations with Hilfer-Katugampola fractional derivativeMohammed. A. Almalahi Satish. K. PanchalIn this work, we present the existence, uniqueness, and stability result of solution to the nonlinear fractional differential equations involving Hilfer-Katugampola derivative subject to nonlocal fractional integral boundary conditions. The reasoning is mainly based upon properties of Mittag-Leffler functions, and fixed-point methods such as Banach contraction principle and Krasnoselskii's fixed point theorem. Moreover, the generalized Gornwall inequality lemma is used to analyze different types of stability. Finally, one example is given to illustrate our theoretical results.https://dergipark.org.tr/tr/download/article-file/961784hilfer--katugampola fractional derivativeexistencemittag-leffler functionsulam stability
collection DOAJ
language English
format Article
sources DOAJ
author Mohammed. A. Almalahi
Satish. K. Panchal
spellingShingle Mohammed. A. Almalahi
Satish. K. Panchal
Existence and stability results of relaxation fractional differential equations with Hilfer-Katugampola fractional derivative
Advances in the Theory of Nonlinear Analysis and its Applications
hilfer--katugampola fractional derivative
existence
mittag-leffler functions
ulam stability
author_facet Mohammed. A. Almalahi
Satish. K. Panchal
author_sort Mohammed. A. Almalahi
title Existence and stability results of relaxation fractional differential equations with Hilfer-Katugampola fractional derivative
title_short Existence and stability results of relaxation fractional differential equations with Hilfer-Katugampola fractional derivative
title_full Existence and stability results of relaxation fractional differential equations with Hilfer-Katugampola fractional derivative
title_fullStr Existence and stability results of relaxation fractional differential equations with Hilfer-Katugampola fractional derivative
title_full_unstemmed Existence and stability results of relaxation fractional differential equations with Hilfer-Katugampola fractional derivative
title_sort existence and stability results of relaxation fractional differential equations with hilfer-katugampola fractional derivative
publisher ATNAA
series Advances in the Theory of Nonlinear Analysis and its Applications
issn 2587-2648
2587-2648
publishDate 2020-10-01
description In this work, we present the existence, uniqueness, and stability result of solution to the nonlinear fractional differential equations involving Hilfer-Katugampola derivative subject to nonlocal fractional integral boundary conditions. The reasoning is mainly based upon properties of Mittag-Leffler functions, and fixed-point methods such as Banach contraction principle and Krasnoselskii's fixed point theorem. Moreover, the generalized Gornwall inequality lemma is used to analyze different types of stability. Finally, one example is given to illustrate our theoretical results.
topic hilfer--katugampola fractional derivative
existence
mittag-leffler functions
ulam stability
url https://dergipark.org.tr/tr/download/article-file/961784
work_keys_str_mv AT mohammedaalmalahi existenceandstabilityresultsofrelaxationfractionaldifferentialequationswithhilferkatugampolafractionalderivative
AT satishkpanchal existenceandstabilityresultsofrelaxationfractionaldifferentialequationswithhilferkatugampolafractionalderivative
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