Shabibi, Mehdi Zada, Akbar Masiha, Hashem Parvaneh Rezapour, Shahram
Published in
Boundary Value Problems

The Sturm–Liouville equation is among the significant differential equations having many applications, and a lot of researchers have studied it. Up to now, different versions of this equation have been reviewed, but one of its most attractive versions is its strong singular version. In this work, we investigate the existence of solutions for the st...

Das, Anupam Suwan, Iyad Deuri, Bhuban Chandra Abdeljawad, Thabet
Published in
Advances in Difference Equations

The aim of this paper is the solvability of generalized proportional fractional(GPF) integral equation at Banach space E\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\...

Laeli Dastjerdi, H.
Published in
Computational and Applied Mathematics

In this paper, we consider blow up and quenching behavior of nonlinear singular Volterra integral equations with vanishing delay. In quenching problems, the solution remains bounded. Instead, the first-order derivative becomes unbounded and blows up in finite time. We present some analytic results. Moreover, we show that there is difference between...

Tunç, Osman
Published in
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas

In this paper, non-perturbed and perturbed systems of non-linear differential equations with multiple constant delays are considered. Five new theorems on the qualitative properties of solutions, uniform asymptotic stability (UAS) and instability of trivial solution, boundedness and integrability of solutions, are obtained. The technique of the pro...

Yang, Guang Shiri, Babak Kong, Hua Wu, Guo-Cheng
Published in
Computational and Applied Mathematics

Fractional differential equation approach is frequently used to describe long-term interactions in nonlinear systems. However, it results in difficulty in inverse problems as well as the numerical treatment. Numerical analysis of intermediate value problems and the well-posedness are investigated in this study. Two high order numerical methods for ...

Cozzi, Matteo Lombardini, Luca
Published in
Calculus of Variations and Partial Differential Equations

We develop a functional analytic approach for the study of nonlocal minimal graphs. Through this, we establish existence and uniqueness results, a priori estimates, comparison principles, rearrangement inequalities, and the equivalence of several notions of minimizers and solutions.

Das, Anupam Hazarika, Bipan Panda, Sumati Kumari Vijayakumar, V.
Published in
Computational and Applied Mathematics

In the current article we obtain the extension of Darbo’s fixed point theorem (DFPT), and apply this theorem to prove the existence of solution of an infinite system of implicit fractional integral equations. We, besides that, justify the results with the help of an example. The advantage of the proposed fixed point theory is that the requirement o...

Tunç, Cemil Tunç, Osman
Published in
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas

In the paper, Tian and Wang (Appl Math Lett 105:106325, 8 pp, 2020, Theorem 1) took into consideration a linear system of integro-delay differential equations (IDDEs) with constant time retardation. In Tian and Wang (2020), the authors proved a new and interesting theorem concerning asymptotically stability of zero solution of that linear system of...

Bellido, José C. Ortega, Alejandro
Published in
Calculus of Variations and Partial Differential Equations

In this work we introduce volume constraint problems involving the nonlocal operator (-Δ)δs\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(-\Delta )_{\delta }^{s}$$\en...

Jin, Kun-Peng Liang, Jin Xiao, Ti-Jun
Published in
Nonautonomous Dynamical Systems

In this paper, we study the global existence of solutions to some semilinear integro-differential evolution equations in Hilbert spaces with sign-varying kernels. By treating the problem through fixed point theory and energy method, we obtain the global existence theorem on [0, +∞) of mild and strong solution to the evolution equations with memory ...