Electron. J. Differential Equations,
Vol. 2017 (2017), No. 145, pp. 1-15.
Integral solutions of fractional evolution equations with nondense domain
Haibo Gu, Yong Zhou, Bashir Ahmad, Ahmed Alsaedi
Abstract:
In this article, we study the existence of integral solutions for two
classes of fractional order evolution equations with nondensely defined
linear operators. First, we consider the nonhomogeneous fractional
order evolution equation and obtain its integral solution by Laplace
transform and probability density function. Subsequently, based on
the form of integral solution for nonhomogeneous fractional order
evolution equation, we investigate the existence of integral solution
for nonlinear fractional order evolution equation by noncompact
measure method.
Submitted March 11, 2017. Published June 19, 2017.
Math Subject Classifications: 26A33, 34K37, 37L05, 47J35.
Key Words: Fractional evolution equation; Caputo derivative;
integral solution; nondense domain.
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Haibo Gu
School of Mathematics Sciences
Xinjiang Normal University
Urumqi, Xinjiang 830054, China
email: hbgu_math@163.com
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Yong Zhou
Faculty of Mathematics and Computational Science
Xiangtan University, Hunan 411105, China
email: yzhou@xtu.edu.cn
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Bashir Ahmad
Nonlinear Analysis and Applied Mathematics (NAAM) Research Group
Faculty of Science, King Abdulaziz University
Jeddah 21589, Saudi Arabia
email: bashirahmad_qau@yahoo.com
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Ahmed Alsaedi
Nonlinear Analysis and Applied Mathematics (NAAM) Research Group
Faculty of Science, King Abdulaziz University
Jeddah 21589, Saudi Arabia
email: aalsaedi@hotmail.com
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