Controllability of Mild Solution of Nonlocal Conformable Fractional Differential Equations
In many research works Bouaouid et al. have proved the existence of mild solutions of an abstract class of nonlocal conformable fractional Cauchy problem of the form: dαxt/dtα=Axt+ft,xt,x0=x0+gx,t∈0,τ. The present paper is a continuation of these works in order to study the controllability of mild s...
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Wiley
2022-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2022/3671909 |
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| author | Mohamed Hannabou Mohamed Bouaouid Khalid Hilal |
| author_facet | Mohamed Hannabou Mohamed Bouaouid Khalid Hilal |
| author_sort | Mohamed Hannabou |
| collection | DOAJ |
| description | In many research works Bouaouid et al. have proved the existence of mild solutions of an abstract class of nonlocal conformable fractional Cauchy problem of the form: dαxt/dtα=Axt+ft,xt,x0=x0+gx,t∈0,τ. The present paper is a continuation of these works in order to study the controllability of mild solution of the above Cauchy problem. Precisely, we shall be concerned with the controllability of mild solution of the following Cauchy problem dαxt/dtα=Axt+ft,xt+But,x0=x0+gx,t∈0,τ, where dα./dtα is the vectorial conformable fractional derivative of order α∈0,1 in a Banach space X and A is the infinitesimal generator of a semigroup Ttt≥0 on X. The element x0 is a fixed vector in X and f, g are given functions. The control function u is an element of L20,τ,U with U is a Banach space and B is a bounded linear operator from U into X. |
| format | Article |
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| institution | Kabale University |
| issn | 1687-9139 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
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| series | Advances in Mathematical Physics |
| spelling | doaj-art-aba7e20a50264b1ab625f5c6252113482025-02-03T01:22:55ZengWileyAdvances in Mathematical Physics1687-91392022-01-01202210.1155/2022/3671909Controllability of Mild Solution of Nonlocal Conformable Fractional Differential EquationsMohamed Hannabou0Mohamed Bouaouid1Khalid Hilal2Sultan Moulay Slimane UniversitySultan Moulay Slimane UniversitySultan Moulay Slimane UniversityIn many research works Bouaouid et al. have proved the existence of mild solutions of an abstract class of nonlocal conformable fractional Cauchy problem of the form: dαxt/dtα=Axt+ft,xt,x0=x0+gx,t∈0,τ. The present paper is a continuation of these works in order to study the controllability of mild solution of the above Cauchy problem. Precisely, we shall be concerned with the controllability of mild solution of the following Cauchy problem dαxt/dtα=Axt+ft,xt+But,x0=x0+gx,t∈0,τ, where dα./dtα is the vectorial conformable fractional derivative of order α∈0,1 in a Banach space X and A is the infinitesimal generator of a semigroup Ttt≥0 on X. The element x0 is a fixed vector in X and f, g are given functions. The control function u is an element of L20,τ,U with U is a Banach space and B is a bounded linear operator from U into X.http://dx.doi.org/10.1155/2022/3671909 |
| spellingShingle | Mohamed Hannabou Mohamed Bouaouid Khalid Hilal Controllability of Mild Solution of Nonlocal Conformable Fractional Differential Equations Advances in Mathematical Physics |
| title | Controllability of Mild Solution of Nonlocal Conformable Fractional Differential Equations |
| title_full | Controllability of Mild Solution of Nonlocal Conformable Fractional Differential Equations |
| title_fullStr | Controllability of Mild Solution of Nonlocal Conformable Fractional Differential Equations |
| title_full_unstemmed | Controllability of Mild Solution of Nonlocal Conformable Fractional Differential Equations |
| title_short | Controllability of Mild Solution of Nonlocal Conformable Fractional Differential Equations |
| title_sort | controllability of mild solution of nonlocal conformable fractional differential equations |
| url | http://dx.doi.org/10.1155/2022/3671909 |
| work_keys_str_mv | AT mohamedhannabou controllabilityofmildsolutionofnonlocalconformablefractionaldifferentialequations AT mohamedbouaouid controllabilityofmildsolutionofnonlocalconformablefractionaldifferentialequations AT khalidhilal controllabilityofmildsolutionofnonlocalconformablefractionaldifferentialequations |