scholarly journals Qualitative Analysis of Multi-Terms Fractional Order Delay Differential Equations via the Topological Degree Theory

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 218 ◽  
Author(s):  
Muhammad Sher ◽  
Kamal Shah ◽  
Michal Fečkan ◽  
Rahmat Ali Khan
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Topological Degree ◽  
Degree Theory ◽  
Qualitative Theory ◽  
Proportional Delay ◽  
Topological Degree Theory ◽  
Fractional Order Differential Equations ◽  
Delay Differential ◽  
Stability Results

With the help of the topological degree theory in this manuscript, we develop qualitative theory for a class of multi-terms fractional order differential equations (FODEs) with proportional delay using the Caputo derivative. In the same line, we will also study various forms of Ulam stability results. To clarify our theocratical analysis, we provide three different pertinent examples.

scholarly journals APPLICABILITY OF TOPOLOGICAL DEGREE THEORY TO EVOLUTION EQUATION WITH PROPORTIONAL DELAY

Fractals ◽  
2020 ◽  
Vol 28 (08) ◽  
pp. 2040028
Author(s):  
MUHAMMAD SHER ◽  
KAMAL SHAH ◽  
YU-MING CHU ◽  
RAHMAT ALI KHAN
Keyword(s):  
Evolution Equation ◽  
Caputo Derivative ◽  
Existence And Uniqueness ◽  
Topological Degree ◽  
Degree Theory ◽  
Proportional Delay ◽  
Ulam Stability ◽  
Topological Degree Theory ◽  
Local Conditions ◽  
Fractional Order Differential Equations

In this paper, we use the topological degree theory (TDT) to investigate the existence and uniqueness of solution for a class of evolution fractional order differential equations (FODEs) with proportional delay using Caputo derivative under local conditions. In the same line, we will also study different kinds of Ulam stability such as Ulam–Hyers (UH) stability, generalized Ulam–Hyers (GUH) stability, Ulam–Hyers–Rassias (UHR) stability and generalized Ulam–Hyers–Rassias (GUHR) stability for the considered problem. To justify our results we provide an example.

scholarly journals Positive Solutions Using Bifurcation Techniques for Boundary Value Problems of Fractional Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Yansheng Liu
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Topological Degree ◽  
Boundary Value ◽  
Degree Theory ◽  
Topological Degree Theory ◽  
Existence Of Positive Solutions ◽  
Fractional Differential

This paper is concerned with the existence of positive solutions for a class of boundary value problems of fractional differential equations with parameter. The main tools used here are bifurcation techniques and topological degree theory. Finally, an example is worked out to demonstrate the main result.

scholarly journals Study of an implicit type coupled system of fractional differential equations by means of topological degree theory

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Muhammad Sarwar ◽  
Anwar Ali ◽  
Mian Bahadur Zada ◽  
Hijaz Ahmad ◽  
Taher A. Nofal
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Topological Degree ◽  
Nonlinear Differential Equations ◽  
Sufficient Conditions ◽  
Degree Theory ◽  
Coupled System ◽  
Sufficient Condition ◽  
Topological Degree Theory ◽  
Fractional Differential

AbstractIn this work, a sufficient condition required for the presence of positive solutions to a coupled system of fractional nonlinear differential equations of implicit type is studied. To study sufficient conditions essential for the existence of unique solution degree theory is used. Two examples are given to illustrate the established results.

scholarly journals Solvability for a Fractional Order Three-Point Boundary Value System at Resonance

2014 ◽  
Vol 2014 ◽  
pp. 1-15
Author(s):  
Zigen Ouyang ◽  
Hongliang Liu
Keyword(s):  
Integral Equation ◽  
Fractional Order ◽  
Topological Degree ◽  
Boundary Value ◽  
Degree Theory ◽  
New Method ◽  
Point Boundary ◽  
Topological Degree Theory ◽  
Value System ◽  
At Resonance

A class of fractional order three-point boundary value system with resonance is investigated in this paper. Using some techniques of inequalities, a completely new method is incorporated. We transform the problem into an integral equation with a pair of undetermined parameters. The topological degree theory is applied to determine the particular value of the parameters so that the system has a solution.

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