The Journal of the Indian Mathematical Society

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Nonlocal Cauchy Problem for Fractional Nonlinear Integrodifferential Equations


Affiliations
1 Department of Mathematics, Sri Ramakrishna Mission Vidyalaya, College of Arts and science, Coimbatore 641 020, India
     

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In this paper we discuss the existence and uniqueness of solutions to the nonlocal fractional nonlinear integrodifferential equations

Dqx(t) = f(t, x(t), ∫t0 a(t,s)h(s, x(s))ds), t ∈ [0, T] x(0) + g(x) = x0, where 0 < q < 1

in a Banach space. We use classical tools from functional analysis to obtain the results.


Keywords

Cauchy Problem, Fractional Integrodifferential Quations, Krasnoselkii Theorem.
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  • Nonlocal Cauchy Problem for Fractional Nonlinear Integrodifferential Equations

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Authors

R. Murugesu
Department of Mathematics, Sri Ramakrishna Mission Vidyalaya, College of Arts and science, Coimbatore 641 020, India
S. Suguna
Department of Mathematics, Sri Ramakrishna Mission Vidyalaya, College of Arts and science, Coimbatore 641 020, India

Abstract


In this paper we discuss the existence and uniqueness of solutions to the nonlocal fractional nonlinear integrodifferential equations

Dqx(t) = f(t, x(t), ∫t0 a(t,s)h(s, x(s))ds), t ∈ [0, T] x(0) + g(x) = x0, where 0 < q < 1

in a Banach space. We use classical tools from functional analysis to obtain the results.


Keywords


Cauchy Problem, Fractional Integrodifferential Quations, Krasnoselkii Theorem.