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14 results on '"Horani, Mohammed Al"'

3. Conformable Fractional Semigroups of Operators

Author

Horani, Mohammed AL, Khalil, Roshdi, and Abdeljawad, Thabet

Subjects
Mathematics - Functional Analysis, Mathematics - Analysis of PDEs, Mathematics - Dynamical Systems
Abstract

Let $X$ be a Banach space, and $T:[0,\infty)\rightarrow {\mathcal{L}}(X,X),$ the bounded linear operators on $X.$ A family $\{T(t)\}_{t\ge 0}\subseteq {% \mathcal{L}}(X,X)$ is called a one-parameter semigroup if $T(s+t)=T(s)T(t),$ and $T(0)=I,$ the identity operator on $X.$ The infinitesimal generator of the semigroup is the derivative of the semigroup at $t=0.$ The object of this paper is to introduce a (conformable) fractional semigroup of operators whose generator will be the fractional derivative of the semigroup at $t=0.$ The basic properties of such semigroups will be studied.

Published
2014

7. Inverse problems on degenerate integro-differential equations.

Author

Horani, Mohammed Al, Favini, Angelo, and Tanabe, Hiroki

Subjects
INVERSE problems, PARTIAL differential equations, EVOLUTION equations, INTEGRO-differential equations
Abstract

We study inverse problems on degenerate integro-differential equations without using maximal regularity property. This seems new at all in the related literature. Some applications to concrete partial differential equations are given. [ABSTRACT FROM AUTHOR]

Published
2022
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8. Degenerate differential problems with fractional derivatives

Author

Horani, Mohammed AL, Favini, Angelo, Horani, Mohammed AL, and Favini, Angelo

Abstract

We describe an extension of previous results on degenerate abstract equations described by Favini and Yagi in their monograph cited in the references.This allows us to study degenerate differential equations with fractional derivative in time. Both direct and relative inverse problems are studied. Finally, various applications to degenerate partial differential equations are described.

Published
2021

10. Fractional Cauchy problems for infinite interval case.

Author

Horani, Mohammed Al, Fabrizio, Mauro, Favini, Angelo, and Tanabe, Hiroki

Subjects
INVERSE problems, PARTIAL differential equations, EVOLUTION equations, DEGENERATE differential equations, CAUCHY problem
Abstract

We are devoted with fractional abstract Cauchy problems. Required conditions on spaces and operators are given guaranteeing existence and uniqueness of solutions. An inverse problem is also studied. Applications from partial differential equations are given to illustrate the abstract fractional degenerate differential problems. [ABSTRACT FROM AUTHOR]

Published
2020
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11. Fractional Cauchy problems and applications.

Author

Horani, Mohammed AL, Fabrizio, Mauro, Favini, Angelo, and Tanabe, Hiroki

Subjects
CAUCHY problem, INVERSE problems, PARTIAL differential equations, EVOLUTION equations, DEGENERATE differential equations
Abstract

We are devoted to fractional abstract Cauchy problems. Required conditions on spaces and operators are given guaranteeing existence and uniqueness of solutions. An inverse problem is also studied. Applications to partial differential equations are given to illustrate the abstract fractional degenerate differential problems. [ABSTRACT FROM AUTHOR]

Published
2020
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12. Conformable Fractional Semigroups of Operators

Author

Horani, Mohammed AL, Khalil, Roshdi, and Abdeljawad, Thabet

Subjects
Mathematics - Functional Analysis, Mathematics - Analysis of PDEs, Mathematics::Operator Algebras, FOS: Mathematics, Dynamical Systems (math.DS), Mathematics - Dynamical Systems, Functional Analysis (math.FA), Analysis of PDEs (math.AP)
Abstract

Let $X$ be a Banach space, and $T:[0,\infty)\rightarrow {\mathcal{L}}(X,X),$ the bounded linear operators on $X.$ A family $\{T(t)\}_{t\ge 0}\subseteq {% \mathcal{L}}(X,X)$ is called a one-parameter semigroup if $T(s+t)=T(s)T(t),$ and $T(0)=I,$ the identity operator on $X.$ The infinitesimal generator of the semigroup is the derivative of the semigroup at $t=0.$ The object of this paper is to introduce a (conformable) fractional semigroup of operators whose generator will be the fractional derivative of the semigroup at $t=0.$ The basic properties of such semigroups will be studied.

Published
2015
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