[PDF] Top 20 Fractional differential equations with causal operators
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Fractional differential equations with causal operators
... This paper is organized as follows. In Section , the existence of solution for problem () is investigated by the successive approximate method. We showed it under the assumption that operator Q satisfies a Lipschitz ... See full document
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Nonlinear fractional differential equations with nonlocal fractional integro-differential boundary conditions
... Theorem . (Krasnoselskii’s fixed point theorem) Let M be a closed, bounded, convex, and nonempty subset of a Banach space X. Let A, B be the operators such that (i) Ax + By ∈ M whenever x, y ∈ M; (ii) A is ... See full document
10
Mild solutions for abstract fractional differential equations with almost sectorial operators and infinite delay
... differential equations have been increasingly used for many mathematical mod- els in probability, engineering, physics, astrophysics, economics, ...differential equations has in recent years been an object of ... See full document
11
Fractional complex transforms for fractional differential equations
... differential equations are viewed as alternative models to nonlinear differ- ential ...economics. Fractional differential equations concerning the Riemann-Liouville fractional operators or ... See full document
12
Approximate Controllability of Impulsive Neutral Functional Differential Equations with State dependent Delay via Fractional Operators
... Let A : D(A) → X be the infinitesimal generator of an analytic semigroup T (t), t ≥ 0, of bounded linear operators on a Banach space X . Let 0 ∈ ρ(A), then it is possible to define the fractional power (−A) ... See full document
8
Variation of Parameters for Causal Operator Differential Equations
... takes the form u t x ( ) , = φ ( x + ct ) + ψ ( x − ct ) , where φ and ψ are twice differentiable functions. Notice that at the vertices of these solutions, u x t ( ) , will not be differentiable. Notice also the ... See full document
20
Fractional differintegral operators of the generalized Mittag-Leffler type function
... of fractional-order differential, integral and difference equations arising in certain problems of mathematical, physical, biological and engineering ...of fractional order differintegral ... See full document
7
Fuzzy Local Fractional Differential Equations
... local fractional integrals and derivatives are appeared in many mathematical and physical problems and have plenty of ...local fractional calculus, and we can easily use the properties local ... See full document
16
On solutions for classes of fractional differential equations
... of fractional calculus is viewed by the RiemannLiouville ...time-space fractional differential ...Riemann-Liouville fractional operators. Also, This type of differential equation ... See full document
8
On the oscillation of Hadamard fractional differential equations
... for fractional differential and difference equations was studied by some authors (see ...certain fractional dynamical systems has gained a high impact in the last few years [14, ...of fractional ... See full document
13
Nonlocal impulsive fractional semilinear differential equations with almost sectorial operators
... impulsive differential equations has undergone rapid development over the years and played a very imortant role in modern applied mathematical models of real processes arising in phenomena studied in ... See full document
11
On a nonlocal problem for fractional differential equations via resolvent operators
... The outline of this paper is as follows. In Section , we recall some definitions on Caputo fractional derivatives, analytic resolvent and the mild solutions to (.). In Section , we establish the existence of ... See full document
12
Approximate controllability of fractional differential equations via resolvent operators
... (H) is equivalent to the approximate controllability of the corresponding homogenous linear system. However, due to the complexity of fractional derivatives, one should be more careful to deal with this ... See full document
11
Techniques for Solving a Certain Class of Partial Differential Equation by Fractional Fourier Transform
... term fractional Fourier transforms is crucial in the study of Mathematics and ...systems, fractional Fourier transforms (generalized form of Fourier ...term fractional Fourier transform for the first ... See full document
16
Random fractional functional differential equations
... In this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the Lipschitz type condition. Moreover, the ... See full document
15
Solution Of Integro-Differential Equation Of The Second Order With The Operators
... Theorem 2. (Existence theorem) .Let the vector functions 𝑓 (𝑡, 𝑥, 𝑥,̇ 𝑦, 𝑦,̇ 𝑧) , 𝑔(𝑡, 𝑥, 𝑥,̇ 𝑤, 𝑤̇) be defined on the domain (1) continuous in 𝑡, 𝑥, 𝑥,̇ 𝑦, 𝑦,̇ 𝑧 ̇ , 𝑤, 𝑤̇ and satisfy the inequalities( 2) to (8)and the ... See full document
17
On solutions of fractional Riccati differential equations
... ods to prove the efficiency of the method. The IRKHSM is very powerful and accurate in obtaining approximate solutions for wide classes of the problem. The approximate solu- tion attained by the IRKHSM is uniformly ... See full document
10
Impulsive Hilfer fractional differential equations
... Nonlinear fractional differential equations can be observed in many areas such as popula- tion dynamics, heat conduction in materials with memory, seepage flow in porous media, autonomous mobile robots, fluid ... See full document
20
Solving STO And KD Equations with Modified Riemann-Liouville Derivative Using Improved (G’/G)-expansion Function Method
... space-time fractional STO and KD ...the fractional STO and KD equations, ...certain fractional variable transfor- mation, such fractional evolution equations can be turned into ... See full document
7
Oscillation criteria of fractional differential equations
... of fractional integrals and fractional derivatives, such as the Riemann-Liouville definition, the Caputo definition, the Liouville definition, the Grünwald-Letnikov definition, the Erdélyi-Kober definition ... See full document
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