Generalized Fixed Point Results with Application to Nonlinear Fractional Differential Equations
The main objective of this paper is to introduce the (<inline-formula> <math display="inline"> <semantics> <mrow> <mi>α</mi> <mo>,</mo> <mi>β</mi> </mrow> </semantics> </math> </inline-formula>)-type <in...
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MDPI AG
2020-07-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/7/1168 |
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| author | Hanadi Zahed Hoda A. Fouad Snezhana Hristova Jamshaid Ahmad |
| author_facet | Hanadi Zahed Hoda A. Fouad Snezhana Hristova Jamshaid Ahmad |
| author_sort | Hanadi Zahed |
| collection | DOAJ |
| description | The main objective of this paper is to introduce the (<inline-formula> <math display="inline"> <semantics> <mrow> <mi>α</mi> <mo>,</mo> <mi>β</mi> </mrow> </semantics> </math> </inline-formula>)-type <inline-formula> <math display="inline"> <semantics> <mi>ϑ</mi> </semantics> </math> </inline-formula>-contraction, (<inline-formula> <math display="inline"> <semantics> <mrow> <mi>α</mi> <mo>,</mo> <mi>β</mi> </mrow> </semantics> </math> </inline-formula>)-type rational <inline-formula> <math display="inline"> <semantics> <mi>ϑ</mi> </semantics> </math> </inline-formula>-contraction, and cyclic (<inline-formula> <math display="inline"> <semantics> <mrow> <mi>α</mi> <mtext>-</mtext> <mi>ϑ</mi> </mrow> </semantics> </math> </inline-formula>) contraction. Based on these definitions we prove fixed point theorems in the complete metric spaces. These results extend and improve some known results in the literature. As an application of the proved fixed point Theorems, we study the existence of solutions of an integral boundary value problem for scalar nonlinear Caputo fractional differential equations with a fractional order in (1,2). |
| first_indexed | 2024-03-10T18:26:52Z |
| format | Article |
| id | doaj.art-99fd9bf2ef2243428eab736f3d8b596e |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T18:26:52Z |
| publishDate | 2020-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-99fd9bf2ef2243428eab736f3d8b596e2023-11-20T06:56:16ZengMDPI AGMathematics2227-73902020-07-0187116810.3390/math8071168Generalized Fixed Point Results with Application to Nonlinear Fractional Differential EquationsHanadi Zahed0Hoda A. Fouad1Snezhana Hristova2Jamshaid Ahmad3Department of Mathematics, College of Science, Taibah University, Al Madina Al Munawara 41411, Saudi ArabiaDepartment of Mathematics, College of Science, Taibah University, Al Madina Al Munawara 41411, Saudi ArabiaDepartment of Applied Mathematics and Modeling, University of Plovdiv “Paisii Hilendarski”, 4000 Plovdiv, BulgariaDepartment of Mathematics, University of Jeddah, P.O. Box 80327, Jeddah 21589, Saudi ArabiaThe main objective of this paper is to introduce the (<inline-formula> <math display="inline"> <semantics> <mrow> <mi>α</mi> <mo>,</mo> <mi>β</mi> </mrow> </semantics> </math> </inline-formula>)-type <inline-formula> <math display="inline"> <semantics> <mi>ϑ</mi> </semantics> </math> </inline-formula>-contraction, (<inline-formula> <math display="inline"> <semantics> <mrow> <mi>α</mi> <mo>,</mo> <mi>β</mi> </mrow> </semantics> </math> </inline-formula>)-type rational <inline-formula> <math display="inline"> <semantics> <mi>ϑ</mi> </semantics> </math> </inline-formula>-contraction, and cyclic (<inline-formula> <math display="inline"> <semantics> <mrow> <mi>α</mi> <mtext>-</mtext> <mi>ϑ</mi> </mrow> </semantics> </math> </inline-formula>) contraction. Based on these definitions we prove fixed point theorems in the complete metric spaces. These results extend and improve some known results in the literature. As an application of the proved fixed point Theorems, we study the existence of solutions of an integral boundary value problem for scalar nonlinear Caputo fractional differential equations with a fractional order in (1,2).https://www.mdpi.com/2227-7390/8/7/1168fixed pointcomplete metric spacefractional differential equations |
| spellingShingle | Hanadi Zahed Hoda A. Fouad Snezhana Hristova Jamshaid Ahmad Generalized Fixed Point Results with Application to Nonlinear Fractional Differential Equations Mathematics fixed point complete metric space fractional differential equations |
| title | Generalized Fixed Point Results with Application to Nonlinear Fractional Differential Equations |
| title_full | Generalized Fixed Point Results with Application to Nonlinear Fractional Differential Equations |
| title_fullStr | Generalized Fixed Point Results with Application to Nonlinear Fractional Differential Equations |
| title_full_unstemmed | Generalized Fixed Point Results with Application to Nonlinear Fractional Differential Equations |
| title_short | Generalized Fixed Point Results with Application to Nonlinear Fractional Differential Equations |
| title_sort | generalized fixed point results with application to nonlinear fractional differential equations |
| topic | fixed point complete metric space fractional differential equations |
| url | https://www.mdpi.com/2227-7390/8/7/1168 |
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