In this paper, we consider a multiterm semilinear fractional boundary value problem involving Caputo fractional derivatives and investigate the existence of positive solutions by terms of different given conditions. To do this, we first study the properties of Green’s function, and then by defining two lower and upper control functions and using the wellknown Schauder’s fixed-point theorem, we obtain the desired existence criteria. At the end of the paper, we provide a numerical example based on the given boundary value problem and obtain its upper and lower solutions, and finally, we compare these positive solutions with exact solution graphically.

In the present paper, we consider an important problem from the point of view of application in sciences and engineering, namely, Riemann-Liouville nonlinear fractional boundary value problem. Under new minimal conditions on the parameters 0 ≤ s, 𝜏 ≤ 1, it is shown that, based on the upper and lower solutions method using Schauder fixed point theorem, the positive solutions in a Sobolev spaces exist. Moreover, our results are illustrated by a numerical example.

The objective of this work is to analyze some criteria of the existence of positive solutions for a fractional configuration of the semilinear differential equation equipped with the Riemann‐Liouville operator. To achieve our aim, we first introduce an operator and transform our main problems into equivalent fixed point problems. After that, based on the fixed point theorem attributed to Krasnoselskii and the nonlinear alternative of Leray‐Schauder in a cone, we prove our main results of existence of solutions to our problems in a well‐defined Banach spaces. With the help of illustrative examples at the end of the study, we validate our theoretical outcomes according to the method implemented in theorems.

No abstract

No abstract