scholarly journals Local Existence Theorem of Fractional Differential Equations in Lp Space

2012 ◽  
Vol 9 (2) ◽  
pp. 71-78
Author(s):  
Joseph Abdulahad ◽  
Shayma Murad
Keyword(s):  
Differential Equations ◽  
Existence Theorem ◽  
Fractional Differential Equations ◽  
Local Existence ◽  
Lp Space ◽  
Local Existence Theorem ◽  
Fractional Differential

scholarly journals Existence of the Solution for System of Coupled Hybrid Differential Equations with Fractional Order and Nonlocal Conditions

2016 ◽  
Vol 2016 ◽  
pp. 1-9
Author(s):  
Khalid Hilal ◽  
Ahmed Kajouni
Keyword(s):  
Differential Equations ◽  
Existence Theorem ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Differential Operators ◽  
Nonlocal Conditions ◽  
Uniqueness Result ◽  
Carathéodory Conditions ◽  
Fractional Differential ◽  
Hybrid Differential Equations

This paper is motivated by some papers treating the fractional hybrid differential equations with nonlocal conditions and the system of coupled hybrid fractional differential equations; an existence theorem for fractional hybrid differential equations involving Caputo differential operators of order1<α≤2is proved under mixed Lipschitz and Carathéodory conditions. The existence and uniqueness result is elaborated for the system of coupled hybrid fractional differential equations.

scholarly journals Existence theorem for a unique solution to a coupled system of impulsive fractional differential equations in complex-valued fuzzy metric spaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Humaira ◽  
Hasanen A. Hammad ◽  
Muhammad Sarwar ◽  
Manuel De la Sen
Keyword(s):  
Differential Equations ◽  
Existence Theorem ◽  
Unique Solution ◽  
Fractional Differential Equations ◽  
Metric Spaces ◽  
Coupled System ◽  
Fuzzy Metric ◽  
Impulsive Fractional Differential Equations ◽  
Fractional Differential ◽  
Complex Valued

AbstractIn this manuscript, the existence theorem for a unique solution to a coupled system of impulsive fractional differential equations in complex-valued fuzzy metric spaces is studied and the fuzzy version of some fixed point results by using the definition and properties of a complex-valued fuzzy metric space is presented. Ultimately, some appropriate examples are constructed to illustrate our theoretical results.

Well-posedness of general Caputo-type fractional differential equations

2018 ◽  
Vol 21 (3) ◽  
pp. 819-832 ◽  
Author(s):  
Chung-Sik Sin
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Initial Value Problems ◽  
Fractional Derivatives ◽  
Local Existence ◽  
Well Posedness ◽  
Initial Value ◽  
Uniqueness Of Solutions ◽  
Fractional Differential

Abstract In the present paper, initial value problems of fractional differential equations are considered. The fractional derivatives are defined as the general Caputo-type fractional derivatives proposed by Anatoly Kochubei. By using the Schauder fixed point theorem, the local existence, the global existence and the uniqueness of solutions are obtained under appropriate conditions. In addition, it is proved that the solution depends on the parameters of the equation in a continuous way.

scholarly journals On some semilinear equations of Schrödinger type

2002 ◽  
Vol 90 (1) ◽  
pp. 139
Author(s):  
Rossella Agliardi ◽  
Daniela Mari
Keyword(s):  
Differential Equations ◽  
Existence Theorem ◽  
Sobolev Spaces ◽  
Initial Value Problem ◽  
Local Existence ◽  
Weighted Sobolev Spaces ◽  
Initial Value ◽  
Semilinear Equations ◽  
Local Existence Theorem

We study the initial value problem for some semilinear pseudo-differential equations of the form $\partial _tu + i\ H(x,D_x)u = F(u,\nabla u)$. The assumptions we make on $H$ are trivially satisfied by $\Delta$, thus our equations generalize Schrdinger type equations. A local existence theorem is proved in some weighted Sobolev spaces.

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