This work investigates the existence and uniqueness of solutions for a coupled system fractional differential equations with three-point generalized integral boundary conditions within proportional derivatives Riemann-Liouville type. By using Schauder Banach fixed point theorems, we study aforesaid system. Finally, present an example to validate our theoretical outcomes.

In this paper, we establish some new properties of (?,c)-periodic and asymptotically functions, then apply them to study the existence uniqueness mild solutions these types following semilinear fractional differential equations: (1) {cDt?u(t)=Au(t)+cDt??1f(t,u(t)),1<?<2,t?R,u(0)=0(1) (2) {cDt?u(t)=Au(t)+cDt??1f(t,u(t?h)),1<?<2,t,h?R+,u(0)=0(2) where cDt?(?)(1<?<2) stands for Caputo derivative A...

Abstract A newly proposed p -Laplacian nonperiodic boundary value problem is studied in this research paper the form of generalized Caputo fractional derivatives. The existence and uniqueness solutions are fully investigated for using some fixed point theorems such as Banach Schauder. This work supported with an example to apply all obtained new results validate their applicability.

This paper is devoted to investigating one type of nonlinear two-term fractional order delayed differential equations involving Caputo derivatives. The Leray–Schauder alternative fixed-point theorem and Banach contraction principle are applied analyze the existence uniqueness solutions problem with infinite delay. Additionally, Hyers–Ulam stability considered for delay conditions.

The aim of this special issue is to focus on recent developments and achievements in the theory of function spaces, sequences spaces and their geometry, and compact operators and their applications in various fields of applied mathematics, engineering, and other sciences. The theory of sequence spaces is powerful tool for obtaining positive results concerning Schauder basis and plays a fundamen...

The existence of stationary distributions to distribution dependent stochastic differential equations are investigated by using the ergodicity associated decoupled equation and Schauder fixed point theorem. By Zvonkin's transformation, we also establish result for with singular coefficients. Instead uniqueness, non-uniqueness considered regular Concrete examples including McKean-Vlasov quadrati...

An optimal control problem for a semilinear parabolic partial differential equation with memory is considered. The well-posedness as well the first and second order differentiability of state established by means Schauder fixed point theorem implicity function theorem. For corresponding quadratic cost functional, existence proved. necessary conditions are presented, including investigation adjo...

Abstract We study the Stokes problem for incompressible fluid with mixed nonlinear boundary conditions of subdifferential type. The latter involve a unilateral condition, Navier slip nonmonotone version Navier–Fujita and threshold leak condition frictional weak form leads to new class variational–hemivariational inequalities on convex sets velocity field. Solution existence compactness solution...

In this paper, we consider the existence and uniqueness of global solutions for non-autonomous evolution equations with state-dependent nonlocal conditions, in which undelayed part admits an operator. We discuss problems by utilizing theory operators, Schauder fixed point theorem Banach theorem. Some new results on considered equation are obtained infinite internal [0,+?). end, applied to a cla...