Existence and uniqueness of mild solutions to a semilinear integrodifferential equation of fractional order |
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| Authors: | Yong-Kui Chang V Kavitha M Mallika Arjunan |
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| Institution: | aDepartment of Mathematics, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, PR China;bDepartment of Mathematics, Karunya University, Karunya Nagar, Coimbatore-641 114, Tamil Nadu, India |
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| Abstract: | In this paper, we prove some existence and uniqueness of mild solutions for a semilinear integrodifferential equation of fractional order with nonlocal initial conditions in α-norm. We assume that the linear part generates a noncompact analytic semigroup. Our results cover the cases that the nonlinearity F takes values in different spaces such as X,Xα and Xβ, where α≤β (0,1). Finally, some practical consequences are also obtained. |
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| Keywords: | Fractional differential equation Nonlocal initial conditions Existence and uniqueness Fixed point |
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