Positive solutions for generalized Caputo fractional differential equations using lower and upper solutions method

https://doi.org/10.48185/jfcns.v1i1.78

Authors

  • Hanan A. Wahash Dr. Babasaheb Ambedkar Marathwada University
  • Satish K. Panchal

Keywords:

$\varsigma$-Caputo fractional differential equations, positive solutions, upper and lower solutions, fixed point theorem

Abstract

The existence and uniqueness of positive solutions are investigated for a new class of boundary value problems for a fractional differential equation involving generalized Caputo fractional derivative of order $\vartheta$ ($1<\vartheta\leq2$). Our approach
relies on the properties of a green function, Banach's contraction principle, and Schauder's fixed point technique on a cone. Moreover, we use building the upper and lower control functions for analysis of the results of our suggested problem. In the end, two examples
are given to justify our acquired results.

Published

2020-12-29 — Updated on 2020-12-30

How to Cite

Wahash, H. A., & Panchal, S. K. (2020). Positive solutions for generalized Caputo fractional differential equations using lower and upper solutions method. Journal of Fractional Calculus and Nonlinear Systems, 1(1), 1–12. https://doi.org/10.48185/jfcns.v1i1.78