Results for double phase problem with fractional differential equations

Abstract

In this manuscript, our main focus is present on the existence and multiplicity results concerning a new set of fractional differential equations with double phase problem in the $\psi$-fractional space, $S_H^{\alpha ,\beta ;\psi }\left(\Omega \right)$. We also, we discuss a property for the double phase operator $K_{\psi }^{\alpha ,\beta }\left(\cdot \right)$ and make some comments on the results obtained by the parameters $\alpha ,\beta$ and the function $\psi \left(\cdot \right)$.