Abstract We study distributed optimal control problems, governed by space-time fractional parabolic equations (STFPEs) involving time-fractional Caputo derivatives and spatial of Sturm-Liouville type. first prove existence uniqueness solutions STFPEs on an open bounded interval their regularity. Then we show to a quadratic problem. derive adjoint problem using the right-Caputo derivative in tim...

In the current contribution, an appropriate quantity connected to space of all convergent sequences is provided and shown be a measure noncompactness in Banach space. Through application fixed point theorems Darbo Meir–Keeler, this amount used discuss whether solution infinite system fractional Sturm–Liouville operators exists. We offer numerical example as key finding study.

We consider a conformable fractional Sturm-Liouville problem with the discontinuous(or jump) condition inside interval. The asymptotic formulas for eigenvalues, nodal parameters (nodal points and lengths) of this are calculated by modified Pr?fer substitutions. Also, using these formulas, an explicit formula potential functions is given. After all, we discuss Lipschitz stability considered prob...