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Weakly singular integral inequalities and global solutions for fractional differential equations of Riemann-Liouville type

Zhu Tao

Abstract

In this paper, we obtain some new results about weakly singular integral inequalities. These inequalities are used to discuss the global existence and uniqueness results for fractional differential equations of Riemann-Liouville type. Some examples are provided to illustrate the applicability of our main results.

Weakly singular integral inequalities and global solutions for fractional differential equations of Riemann-Liouville type

Abstract

In this paper, we obtain some new results about weakly singular integral inequalities. These inequalities are used to discuss the global existence and uniqueness results for fractional differential equations of Riemann-Liouville type. Some examples are provided to illustrate the applicability of our main results.

Paper Structure

This paper contains 3 sections, 13 theorems, 86 equations.

Table of Contents

  1. Introduction
  2. weakly singular integral inequalities
  3. global solutions for fractional differential equation

Key Result

Theorem 2.1

Let $p\geq 1$, let $a(t), b(t)\in C[0,T)$$(0<T\leq+\infty)$ be nonnegative, nondecreasing functions, let $l(t)\in C(0,T)\bigcap L^{1}_{Loc}[0,T)$ be a nonnegative function, and let $\omega\in C[0,+\infty)$ be a nondecreasing, nonnegative function. Assume that $u(t)$ is a continuous and nonnegative f Then where $\Omega(x)=\int_{1}^{x}\frac{1}{\mu(t)}dt$, $\mu(t)=\omega(2^{1-\frac{1}{p}}t^{\frac{1}

Theorems & Definitions (34)

  • Theorem 2.1
  • proof
  • Corollary 2.2
  • Theorem 2.3
  • proof
  • Theorem 2.4
  • proof
  • Theorem 2.5
  • proof
  • Corollary 2.6
  • ...and 24 more