Electron. J. Differential Equations, Vol. 2020 (2020), No. 132, pp. 1-16.
Existence and stability for fractional order pantograph equations with nonlocal conditions
Israr Ahmad, Juan Jose Nieto, Ghaus ur Rahman, Kamal Shah
Abstract:
In this article we study the a coupled system of fractional pantograph differential
equations (FPDEs). Using degree theory, we state necessary conditions for the existence of
solutions to a coupled system of fractional partial differential equations with non-local
boundary conditions. Also using tools from non-linear analysis, we establish some stability
results. We illustrate our theoretical results with a test problem.
Submitted December 11, 2019. Published December 26, 2020.
Math Subject Classifications: 26A33, 34A08, 35R11.
Key Words: Coupled system; non-local boundary conditions; stability theory;
pantograph equation.
DOI: 10.58997/ejde.2020.132
An addendum was posted on July 26, 2021. It concerns Theorem 3.1, Corollary 3.2, and
Lemma 3.3. See the last page of this article.
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Israr Ahmad
Department of Mathematics
University of Malakand, Chakdara
Dir(L), Khyber Pakhtunkhwa, Pakistan
email: israrahmadjc503@gmail.com
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Juan Jose Nieto
Instituto de Matemeticas
Universidade de Santiago de Compostela
Santiago de Compostela, 15782, Spain
email: juanjose.nieto.roig@usc.es
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Ghaus ur Rahman
Department of Mathematics and Statistics
University of Swat
Khyber Pakhtunkhwa, Pakistan
email: ghaus957@yahoo.com
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Kamal Shah
Department of Mathematics
University of Malakand, Chakdara
Dir(L), Khyber Pakhtunkhwa, Pakistan
email: kamalshah408@gmail.com
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