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Fractional differential equations
Open AccessArticle

Positive solutions for nonlinear Caputo-Hadamard fractional relaxation differential equations

Annals of Communications in Mathematics 2021

, 4 (3)

, 226-236

DOI: https://doi.org/10.62072/acm.2021.040302

AbstractWe study the existence and uniqueness of positive solutions of the nonlinearfractional relaxation differential equation where Dα/1 is the Caputo-Hadamard fractional derivative of order 0 < α ≤ 1. In the process we convert the given fractional differential equation into an equivalent integral equation. Then we construct an appropriate mapping and employ the Schauder fixed point theorem and the method of upper and lower solutions to show the existence of a positive solution of this equation. We also use the Banach fixed point theorem to show the existence of a unique positive solution. Finally, an example is given to illustrate our results.
Open AccessArticle

Existence of solutions for Hadamard fractional differential equations in Banach spaces

Annals of Communications in Mathematics 2021

, 4 (1)

, 1-9

DOI: https://doi.org/10.62072/acm.2021.040101

AbstractIn this work, we investigate the existence of solutions for Hadamard fractional differential equations with integral boundary conditions in a Banach space. We will make use the measure of noncompactness and the Monch fixed point theorem to prove the ¨ main results. An example is given to illustrate our results.