Existence Theory to a Coupled System of Higher Order Fractional Hybrid Differential Equations by Topological Degree Theory

2018 ◽  
Vol 4 (4) ◽  
Author(s):  
Mian Bahadur Zada ◽  
Kamal Shah ◽  
Rahmat Ali Khan
Keyword(s):  
Differential Equations ◽  
Topological Degree ◽  
Degree Theory ◽  
Coupled System ◽  
Higher Order ◽  
Existence Theory ◽  
Topological Degree Theory ◽  
Hybrid Differential Equations

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 Existence of solutions for a coupled system of fractional differential equations by means of topological degree theory

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Jingli Xie ◽  
Lijing Duan
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Topological Degree ◽  
Existence Of Solutions ◽  
Degree Theory ◽  
Coupled System ◽  
Topological Degree Theory ◽  
Fractional Differential

AbstractThis paper investigates the existence of solutions for a coupled system of fractional differential equations. The existence is proved by using the topological degree theory, and an example is given to show the applicability of our main result.

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 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 on Implicit-Type Fractional Coupled System with Integral Boundary Conditions

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 300
Author(s):  
Longfei Lin ◽  
Yansheng Liu ◽  
Daliang Zhao
Keyword(s):  
Boundary Conditions ◽  
Topological Degree ◽  
Fractional Derivatives ◽  
Existence Result ◽  
Degree Theory ◽  
Integral Boundary Conditions ◽  
Coupled System ◽  
Topological Degree Theory ◽  
Caputo Fractional Derivatives ◽  
Integral Boundary

This paper is concerned with a class of implicit-type coupled system with integral boundary conditions involving Caputo fractional derivatives. First, the existence result of solutions for the considered system is obtained by means of topological degree theory. Next, Ulam–Hyers stability and generalized Ulam–Hyers stability are studied under some suitable assumptions. Finally, one example is worked out to illustrate the main results.

Sign in / Sign up

Export Citation Format

Share Document