Abstract
In this study, we present some results concerning the existence of weak solutions for some coupled systems of Hadamard fractional differential equations involving the both retarded and advanced arguments. Our results are obtained by using fixed point theory and the technique of measure of weak noncompactness.
Highlights
Fractional differential equations have recently been applied in various areas of engineering, mathematics, physics and bio-engineering and other applied sciences (Hilfer, 2000; Tarasov, 2010)
For some fundamental results in the theory of fractional calculus and fractional differential equations we refer the reader to the monographs (Abbas et al, 2012; 2015; Ahmad and Ntouyas, 2015; Kilbas et al, 2006; Thiramanus et al, 2014; Zhou, 2014)
The measure of weak noncompactness is introduced by De Blasi (1977)
Summary
Fractional differential equations have recently been applied in various areas of engineering, mathematics, physics and bio-engineering and other applied sciences (Hilfer, 2000; Tarasov, 2010). In (Agarwal et al, 2016), the authors studied the existence and uniqueness of solutions for boundary value problems of Hadamard-type fractional functional differential equations and inclusions involving both retarded and advanced arguments. In (Abbas et al, 2017), the authors discuss the existence of weak solutions for the following boundary value problem for implicit Pettis Hadamard fractional differential equation:
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