On Ulam’s Stability for a Coupled Systems of Nonlinear Implicit Fractional Differential Equations
In this manuscript, we study the existence, uniqueness and various kinds of Ulam stability including Ulam–Hyers stability, generalized Ulam–Hyers stability, Ulam–Hyers–Rassias stability and generalized Ulam–Hyers–Rassias stability of the solutions to a nonlinear coupled systems of implicit fractiona...
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| Veröffentlicht in: | Bulletin of the Malaysian Mathematical Sciences Society 2019-09, Vol.42 (5), p.2681-2699 |
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| creator | Ali, Zeeshan Zada, Akbar Shah, Kamal |
| description | In this manuscript, we study the existence, uniqueness and various kinds of Ulam stability including Ulam–Hyers stability, generalized Ulam–Hyers stability, Ulam–Hyers–Rassias stability and generalized Ulam–Hyers–Rassias stability of the solutions to a nonlinear coupled systems of implicit fractional differential equations involving Caputo derivative. We develop conditions for uniqueness and existence by using the classical fixed point theorems such as Banach contraction principle and Leray–Schauder of cone type. For stability, we utilize classical functional analysis. Also, an example is given to demonstrate our main theoretical results. |
| doi_str_mv | 10.1007/s40840-018-0625-x |
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We develop conditions for uniqueness and existence by using the classical fixed point theorems such as Banach contraction principle and Leray–Schauder of cone type. For stability, we utilize classical functional analysis. 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Malays. Math. Sci. Soc</stitle><date>2019-09-15</date><risdate>2019</risdate><volume>42</volume><issue>5</issue><spage>2681</spage><epage>2699</epage><pages>2681-2699</pages><issn>0126-6705</issn><eissn>2180-4206</eissn><abstract>In this manuscript, we study the existence, uniqueness and various kinds of Ulam stability including Ulam–Hyers stability, generalized Ulam–Hyers stability, Ulam–Hyers–Rassias stability and generalized Ulam–Hyers–Rassias stability of the solutions to a nonlinear coupled systems of implicit fractional differential equations involving Caputo derivative. We develop conditions for uniqueness and existence by using the classical fixed point theorems such as Banach contraction principle and Leray–Schauder of cone type. For stability, we utilize classical functional analysis. 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| identifier | ISSN: 0126-6705 |
| ispartof | Bulletin of the Malaysian Mathematical Sciences Society, 2019-09, Vol.42 (5), p.2681-2699 |
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| source | SpringerNature Journals |
| subjects | Applications of Mathematics Differential equations Existence theorems Fixed points (mathematics) Functional analysis Mathematical analysis Mathematics Mathematics and Statistics Nonlinear equations Nonlinear systems Stability analysis Uniqueness |
| title | On Ulam’s Stability for a Coupled Systems of Nonlinear Implicit Fractional Differential Equations |
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