A differential intermediate value theorem

SOME FUNDAMENTAL RESULTS ON FUZZY CALCULUS

In this paper, we study fuzzy calculus in two main branches differential and integral.  Some rules for finding limit and $gH$-derivative of $gH$-difference, constant multiple of two fuzzy-valued functions are obtained and we also present fuzzy chain rule for calculating  $gH$-derivative of a composite function.  Two techniques namely,  Leibniz's rule and integration by parts are introduced for ...

On intermediate value theorem in ordered Banach spaces for noncompact and discontinuous mappings

In this paper, a vector version of the intermediate value theorem is established. The main theorem of this article can be considered as an improvement of the main results have been appeared in [textit{On fixed point theorems for monotone increasing vector valued mappings via scalarizing}, Positivity, 19 (2) (2015) 333-340] with containing the uniqueness, convergent of each iteration to the fixe...

Existence of positive solutions for a boundary value problem of a nonlinear fractional differential equation

This paper presents conditions for the existence and multiplicity of positive solutions for a boundary value problem of a nonlinear fractional differential equation. We show that it has at least one or two positive solutions. The main tool is Krasnosel'skii fixed point theorem on cone and fixed point index theory.

Triple Positive Solutions for Boundary Value Problem of a Nonlinear Fractional Differential Equation

Studies on Sturm-Liouville boundary value problems for multi-term fractional differential equations

  Abstract.   The Sturm-Liouville boundary value problem of the multi-order fractional differential equation  is studied. Results on the existence of solutions are established. The analysis relies on a weighted function space and a fixed point theorem. An example is given to illustrate the efficiency of the main theorems.