Well‐posedness of degenerate differential equations with fractional derivative in vector‐valued functional spaces
Sign Up to like & getrecommendations! Published in 2017 at "Mathematische Nachrichten"
DOI: 10.1002/mana.201500481
Abstract: In this paper, we study the well-posedness of the degenerate differential equations with fractional derivative Dα(Mu)(t)=Au(t)+f(t),(0≤t≤2π) in Lebesgue–Bochner spaces Lp(T;X), periodic Besov spaces Bp,qs(T;X) and periodic Triebel–Lizorkin spaces Fp,qs(T;X), where A and M are closed… read more here.
Keywords: degenerate differential; well posedness; fractional derivative; posedness degenerate ... See more keywords
Prolongation of solutions of measure differential equations and dynamic equations on time scales
Sign Up to like & getrecommendations! Published in 2019 at "Mathematische Nachrichten"
DOI: 10.1002/mana.201700420
Abstract: In this paper, we prove the results on existence and uniqueness of the maximal solutions for measure differential equations, considering more general conditions on functions f and g by using the correspondence between the solutions… read more here.
Keywords: time scales; solutions measure; differential equations; dynamic equations ... See more keywords
Notes on the existence and uniqueness of solutions of Stieltjes differential equations
Sign Up to like & getrecommendations! Published in 2021 at "Mathematische Nachrichten"
DOI: 10.1002/mana.201900138
Abstract: We study some classical uniqueness and existence results, such as Peano's or Osgood's uniqueness criteria, in the context of Stieltjes differential equations. This type of equation is based on derivatives with respect to monotone functions,… read more here.
Keywords: existence uniqueness; notes existence; uniqueness solutions; solutions stieltjes ... See more keywords
Existence of positive solutions for integral boundary value problems of fractional differential equations on infinite interval
Sign Up to like & getrecommendations! Published in 2017 at "Mathematical Methods in The Applied Sciences"
DOI: 10.1002/mma.4106
Abstract: In this paper, we consider a class of nonlinear fractional differential equations on the infinite interval D0+αu(t)+ft,u(t),D0+α−1u(t)=0,t∈(0,+∞), with the integral boundary conditions u(0)=0,D0+α−1u(∞)=∫0τg1(s)u(s)ds+a,D0+α−2u(0)=∫0τg2(s)u(s)ds+b. By using Krasnoselskii fixed point theorem, the existence results of positive solutions… read more here.
Keywords: infinite interval; positive solutions; integral boundary; fractional differential ... See more keywords
Multi‐valued backward stochastic differential equations driven by G‐Brownian motion and its applications
Sign Up to like & getrecommendations! Published in 2017 at "Mathematical Methods in The Applied Sciences"
DOI: 10.1002/mma.4335
Abstract: In this paper, we prove the existence and uniqueness of a solution for a class of backward stochastic differential equations driven by G-Brownian motion with subdifferential operator by means of the Moreau–Yosida approximation method. Moreover,… read more here.
Keywords: stochastic differential; backward stochastic; brownian motion; equations driven ... See more keywords
Sturm-Picone comparison theorems for nonlinear impulsive differential equations with discontinuous solutions
Sign Up to like & getrecommendations! Published in 2017 at "Mathematical Methods in The Applied Sciences"
DOI: 10.1002/mma.4571
Abstract: The nonlinear versions of Sturm-Picone comparison theorem as well as Leighton's variational lemma and Leighton's theorem for regular and singular nonlinear impulsive differential equations with discontinuous solutions having fixed moments of impulse actions are established.… read more here.
Keywords: sturm picone; nonlinear impulsive; impulsive differential; differential equations ... See more keywords
Fractional differential equations with a Caputo derivative with respect to a Kernel function and their applications
Sign Up to like & getrecommendations! Published in 2018 at "Mathematical Methods in The Applied Sciences"
DOI: 10.1002/mma.4617
Abstract: R. Almeida was supported by Portuguese funds through the CIDMA-Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology (FCT-Fundacao para a Ciencia e a Tecnologia), within project… read more here.
Keywords: respect kernel; equations caputo; caputo derivative; fractional differential ... See more keywords
Renormalization group second‐order approximation for singularly perturbed nonlinear ordinary differential equations
Sign Up to like & getrecommendations! Published in 2018 at "Mathematical Methods in The Applied Sciences"
DOI: 10.1002/mma.5107
Abstract: Abstract]We consider a two time scale nonlinear system of ordinary differential equations. The small parameter of the system is the ratio ε of the time scales. We search for an approximation involving only the slow… read more here.
Keywords: ordinary differential; order; order approximation; time ... See more keywords
On positive solutions of fractional differential equations with change of sign
Sign Up to like & getrecommendations! Published in 2019 at "Mathematical Methods in the Applied Sciences"
DOI: 10.1002/mma.5619
Abstract: We study the existence and uniqueness of positive solutions of fractional differential equations with change of sign D0+α(u′′(t))=h(t)f(u(t)),0 read more here.
Keywords: change sign; solutions fractional; positive solutions; equations change ... See more keywords
A numerical‐analytical solution of multi‐term fractional‐order differential equations
Sign Up to like & getrecommendations! Published in 2020 at "Mathematical Methods in the Applied Sciences"
DOI: 10.1002/mma.6242
Abstract: In this paper, a solution to initial value problems for fractional‐order linear commensurate multi‐term differential equations with Caputo derivatives is presented. The solution is obtained in the form of a finite sum of the Mittag‐Leffler–type… read more here.
Keywords: numerical analytical; fractional order; solution; multi term ... See more keywords
Existence of solutions for some non‐Fredholm integro‐differential equations with the bi‐Laplacian
Sign Up to like & getrecommendations! Published in 2020 at "Mathematical Methods in the Applied Sciences"
DOI: 10.1002/mma.6721
Abstract: We prove the existence of solutions for some semilinear elliptic equations in the appropriate H4 spaces using the fixed‐point technique where the elliptic equation contains fourth‐order differential operators with and without Fredholm property, generalizing the… read more here.
Keywords: solutions non; integro differential; non fredholm; fredholm integro ... See more keywords