[PDF] Top 20 Existence of the classical and strong solutions for fractional semilinear initial value problems
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Existence of the classical and strong solutions for fractional semilinear initial value problems
... practical problems in many fields such as polymer rheology, chemistry physics, heat conduction, fluid flows, electrical networks, and many other branches of science (see [1, 2, 12, ...the fractional calculus ... See full document
13
Existence of strong solutions for a class of semilinear evolution equations with nonlocal initial conditions
... the existence and uniqueness of mild solutions for evolution equations with nonlocal conditions, there are very few papers considered the regularity results for nonlocal evolution ...the existence of ... See full document
9
On the existence of positive solutions for generalized fractional boundary value problems
... of fractional derivatives such as ψ -Hilfer fractional derivative, Hilfer–Katugampola frac- tional derivative, and generalized proportional fractional derivative [1, 2, 12, 14–17, 23, ...-Hilfer ... See full document
20
Periodic boundary value problems for fractional semilinear integro-differential equations with non-instantaneous impulses
... In [18–20], differential equations are all integer order, the linear operator A is indepen- dent of t, and the semigroup is compact. In [24–26], the linear operator A is independent of t. In this paper, we consider the ... See full document
14
Impulsive initial value problems for a class of implicit fractional differential equations
... impulsive initial value problems for a class of implicit fractional differential equations involving the Caputo fractional derivative of order β ∈ (1, ...The solutions of this ... See full document
14
On boundary value problems of higher order abstract fractional integro-differential equations
... flow problems, control theory, aerodynamics, nonlinear oscillation of earthquake, the fluid-dynamic traffic model, ...by fractional derivatives, see for examples [8, ...on fractional calculus and ... See full document
20
Existence and approximate solutions for hybrid fractional integro-differential equations
... The rest of the paper will be organized as follows. In Section 2 we give some preliminaries and key fixed point theorems that will be used in subsequent part of the paper. In Section 3 we discuss the main ... See full document
10
The existence of solutions to a class of boundary value problems with fractional difference equations
... discrete fractional calculus have appeared, such as [–], which has helped to build up some of the basic theory of this ...for fractional delta-operators and the commutativity of fractional sums ... See full document
20
Existence and uniqueness of mild solutions to initial value problems for fractional evolution equations
... Fractional differential equations have been widely applied in many important areas, in- cluding thermodynamics, porous media, plasma dynamics, cosmic rays, continuum me- chanics, electrodynamics, quantum mechanics, ... See full document
13
On decay and blow-up of solutions for a nonlinear beam equation with double damping terms
... the initial data of a generalized solution to the problem ...global existence, the authors of [1] used the Galerkin ap- proximation method and the monotonicity method (see ...the existence and ... See full document
17
Existence of solutions to fractional boundary value problems at resonance in Hilbert spaces
... the fractional differential operator is Fredholm with zero-index is established, especially for the first time when the fractional differential operator takes values in an arbitrary Hilbert ... See full document
20
Existence and multiplicity of positive solutions for a system of fractional boundary value problems
... Under sufficient conditions on functions f and g, which can be nonsingular or singular in the points t = and/or t = , we study the existence and multiplicity of positive solutions of problem (S)-(BC). We ... See full document
17
The existence of solutions for nonlinear fractional multipoint boundary value problems at resonance
... the existence of solutions for multipoint boundary value problems (BVPs for short in the remaining) at nonresonance of FDEs (see ...the existence of solutions for a nonlinear ... See full document
14
Existence of solutions of fractional boundary value problems with p-Laplacian operator
... for t ∈ [, ]. Since f , g, h are continuous, the expression () and () are well defined. Clearly, the fixed point of the operator T is the solution of the problem ()-(). To show the existence and uniqueness ... See full document
16
On existence and uniqueness of positive solutions to a class of fractional boundary value problems
... 1. Diethelm, K, Freed, AD: On the solutions of nonlinear fractional order differential equations used in the modelling of viscoplasticity. In: Keil F, Mackens W, Voss H, Werthers J (eds.) Scientific ... See full document
9
Nontrivial solutions for a higher fractional differential equation with fractional multi-point boundary conditions
... Differential equations of fractional order occur more frequently in different research ar- eas such as engineering, physics, chemistry, economics, etc. Indeed, we can find numerous applications in viscoelasticity, ... See full document
16
Multiplicity of positive solutions for Sturm-Liouville boundary value problems of fractional differential equations with p-Laplacian
... f : [0, 1] × [0, +∞) → [0, +∞) is continuous. By means of the properties of the Green’s function, Leggett-Williams fixed-point theorems, and fixed-point index theory, several new sufficient conditions for the ... See full document
17
Studies on Sturm-Liouville boundary value problems for multi-term fractional differential equations
... Caputo’s fractional derivative of order ∗, and f : [0, 1]×[0, +∞) ×R → [0, +∞) is ...cones, existence and multiplicity results of positive solutions of ... See full document
18
Studies on Sturm-Liouville boundary value problems for multi-term fractional differential equations
... sequential fractional differential ...the fractional derivatives, this rep- resents an interesting complication that does not arise in the integer- order ...two fractional derivatives, which gives ... See full document
18
$L^p$-existence of mild solutions of fractional differential equations in Banach space
... of fractional calculus, measure of noncompactness, and fixed point theorem with respect to a k-set-contractive operator, we obtain a new result on the existence of mild solutions with the assumption ... See full document
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