This paper investigates the problem of the existence and uniqueness of solutions under the generalized self-similar forms to the space-fractional diffusion equation. Therefore, through applying the properties of Schauder's and Banach's fixed point theorems; we establish several results on the global existence and blow-up of generalized self-similar solutions to this equation.
Arioua, Yacine, and Bilal Basti, and Nouredine Benhamidouche. "Initial value problem for nonlinear implicit fractional differential equations with Katugampola derivative." Appl. Math. E-Notes 19 (2019): 397-412.
Basti, Bilal, and Yacine Arioua, and Nouredine Benhamidouche. "Existence and uniqueness of solutions for nonlinear Katugampola fractional differential equations." J. Math. Appl. 42 (2019): 35-61.
Basti, Bilal, and Yacine Arioua, and Nouredine Benhamidouche. "Existence results for nonlinear Katugampola fractional differential equations with an integral condition." Acta Math. Univ. Comenian. (N.S.) 89 (2020): 243-260.
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