Existence of positive solutions for weighted fractional order differential equations
By Mohammed S Abdo, Thabet Abdeljawad, Saeed M. Ali, Kamal Shah, Fahd Jarad. 2020
47 citations recorded by the source corpus.
Abstract In this paper, we deliberate two classes of initial value problems for nonlinear fractional differential equations under a version weighted generalized of Caputo fractional derivative given by Jarad et al. (2020a) [25]. We get a formula for the solution through the equivalent fractional integral equations to the proposed problems. The existence and uniqueness of positive solutions have been obtained by using lower and upper solutions. The acquired results are demonstrated by building the upper and lower control functions of the nonlinear term with the aid of Banach and Schauder fixed point theorems. The acquired results are demonstrated by pertinent numerical examples along with the Bashforth Moulton prediction correction scheme and Matlab.
Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/e750bfea25d78e53ab50c6742861fa752338f22c
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In Applied Mathematics
In Modeling and Simulation
In Numerical Analysis
Citations in the corpus
- Weighted Fractional Calculus: A General Class of Operators (2022, background): “For example, a 2020 paper of Al-Refai [11] studied weighted Atangana–Baleanu fractional calculus, and a 2021 paper of Jarad et al [12] studied weighted fractional calculus with respect to functions, and other papers on weighted fractional operators [13, 14, 15] have also been published in the last f”