Fractional Differential Equations with Mixed Boundary Conditions

By Ricardo Almeida. Bulletin of the Malaysian Mathematical Sciences Society, 2017

63 citations recorded by the source corpus.

In this paper, we discuss the existence and uniqueness of solutions of a boundary value problem for a fractional differential equation of order α∈(2,3)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha \in (2,3)$$\end{document}, involving a general form of fractional derivative. First, we prove an equivalence between the Cauchy problem and the Volterra equation. Then, two results on the existence of solutions are proven, and we end with some illustrative examples.

Subfields: Applied Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/1f9a1245943da302400848628b0562e1933b6ec8

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Modeling and Simulation

Citations in the corpus

On the existence of positive solutions for generalized fractional boundary value problems (2019, unknown): “The results of this paper are motivated by the recent work of Almeida in [3] who established results for the existence and uniqueness of solutions of FBVP involving a general form of fractional derivative.”
Nonlinear generalized fractional differential equations with generalized fractional integral conditions (2020, methodology): “As an application managing with the theory of ψ-fractional differentiation, we refer to [15], the reader will find other classifications of ψ-fractional differentiation with various applications in the work [16–18] In [19], Almeida investigate theexistenceanduniqueness of solution for the following ”