Existence of positive solutions for weighted fractional order differential equations

Mohammed S. Abdo, Thabet Abdeljawad, Saeed M. Ali, Kamal Shah and Fahd Jarad

Chaos, Solitons & Fractals, 2020, vol. 141, issue C

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.

Keywords: Fractional differential equation; ψ-weighted Caputo operator; Control functions; Lower and upper solutions; Fixed point theorem (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:141:y:2020:i:c:s0960077920307360

DOI: 10.1016/j.chaos.2020.110341

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