Journal of Integral Equations and Applications

Approximations of solutions to a retarded type fractional differential equation with a deviated argument

Pradeep Kumar, D.N. Pandey, and D. Bahuguna

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In the present work, we are concerned with approximations of solutions to a retarded type fractional differential equation with a deviated argument in a separable Hilbert space~$H$. We consider an integral equation associated with a given problem and then consider a sequence of approximate integral equations. We prove the existence, uniqueness and convergence to each of the approximate integral equations by using analytic semigroup theory and the fixed point method. We also prove that the limiting function satisfies the associated integral equation. Finally, we consider Faedo-Galerkin approximations of solutions and prove some convergence results.

Article information

J. Integral Equations Applications, Volume 26, Number 2 (2014), 215-242.

First available in Project Euclid: 21 July 2014

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Primary: 34G10: Linear equations [See also 47D06, 47D09] 34G20: Nonlinear equations [See also 47Hxx, 47Jxx] 34K30: Equations in abstract spaces [See also 34Gxx, 35R09, 35R10, 47Jxx] 35K90: Abstract parabolic equations 47N20: Applications to differential and integral equations

Analytic semigroup retarded type fractional differential equation deviated argument Banach fixed point theorem Faedo-Galerkin approximation


Kumar, Pradeep; Pandey, D.N.; Bahuguna, D. Approximations of solutions to a retarded type fractional differential equation with a deviated argument. J. Integral Equations Applications 26 (2014), no. 2, 215--242. doi:10.1216/JIE-2014-26-2-215.

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