Abstract
This paper investigates the existence of the unique solution for a Hadamard fractional integral boundary value problem of a Hadamard fractional integro-differential equation with the monotone iterative technique. Two examples to illustrate our result are given.
Highlights
Fractional differential equations are becoming more and more popular recently in several journals and books due to their applications in a number of fields such as physics, biophysics, mechanical systems, electrical-analytical, and thermal systems [ – ]
In [ ], Hadamard presented a concept of fractional derivatives, which is different from Caputo and Riemann-Liouville type fractional derivatives and involves a logarithmic function of an arbitrary exponent in the integral kernel
It is significant that the study of Hadamard type fractional differential equations is still in its infancy and deserves further study
Summary
Fractional differential equations are becoming more and more popular recently in several journals and books due to their applications in a number of fields such as physics, biophysics, mechanical systems, electrical-analytical, and thermal systems [ – ]. It is significant that the study of Hadamard type fractional differential equations is still in its infancy and deserves further study. A detailed presentation of Hadamard fractional derivative is available in [ ] and [ – ]. We consider the following Hadamard fractional integrodifferential equations with Hadamard fractional integral boundary conditions on an infinite interval: H Dγ u(t) + f (t, u(t), H Iqu(t)) = , < γ < , t ∈ ( , +∞), u( ) = u ( ) = , H Dγ – u(∞) =
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