Abstract
By combining the techniques of fractional calculus with measure of weak noncompactness and fixed point theorem, we establish the existence of weak solutions of multipoint boundary value problem for fractional integrodifferential equations.
Highlights
Fractional differential equations in Banach spaces have been studied and a few papers consider fractional differential equations in reflexive Banach spaces equipped with the weak topology
De Blasi [3] introduced the concept of measure of weak noncompactness and proved the analogue of Sadovskiis fixed point theorem for the weak topology
Motivated by the above works, in this paper, we use the techniques of measure of weak noncompactness combine with the fixed point theorem to discuss the existence theorem of weak solutions for a class of nonlinear fractional integrodifferential equations of the form cDα0+x (t) = f (t, x (t), (Tx) (t), (Sx) (t)), a1x (0) − b1x (0) = d1x (ξ1), t ∈ [0, 1], α ∈ (1, 2], (5)
Summary
Fractional differential equations in Banach spaces have been studied and a few papers consider fractional differential equations in reflexive Banach spaces equipped with the weak topology. B1x (1) + b2x (1) = γ2, and obtain a new result by using the techniques of measure of weak noncompactness and Henstock-Kurzweil-Pettis integrals, where cDα0+ denotes the fractional Caputo derivative and the operators given by s (Tx) (s) = ∫ k1 (s, τ) g (τ, x (τ)) dτ,. Motivated by the above works, in this paper, we use the techniques of measure of weak noncompactness combine with the fixed point theorem to discuss the existence theorem of weak solutions for a class of nonlinear fractional integrodifferential equations of the form a1x (0) − b1x (0) = d1x (ξ1) , t ∈ [0, 1] , α ∈ (1, 2] , (5). We use the techniques of measure of weak noncompactness and Henstock-Kurzweil-Pettis integrals to discuss the existence theorem of weak solutions for a class of the multipoint boundary value problem of fractional integrodifferential equations equipped with the weak topology.
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