Solvability of infinite systems of fractional differential equations in the double sequence space $$ 2^c(\triangle )$$

Abstract

In this work, we first introduce the concept of double sequence space $$2^c(\triangle )$$ . Then, we construct a Hausdorff measure of noncompactness on this space. Furthermore, by employing this measure of noncompactness we discuss the existence of solutions for infinite systems of third-order three-point boundary value problem in the double sequence space $$2^c(\triangle )$$ . Eventually, we demonstrate an example to show the effectiveness and usefulness of the obtained result.