Monotonic solutions for a quadratic integral equation of fractional order
In this paper we present a global existence theorem of a positive monotonic integrable solution for the mixed type nonlinear quadratic integral equation of fractional order\[x(t) = p(t) + h(t,x(t)) \int_{0}^{t} k(t,s)( f_1( s, I^\alpha f_2(s, x(s)))+g_1( s, I^\beta g_2(s, x(s))))ds,~t\in [0,1],\al...
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| Format: | Article |
| Language: | English |
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AIMS Press
2019-07-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/10.3934/math.2019.3.821/fulltext.html |
| _version_ | 1819291751212384256 |
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| author | A. M. A. El-Sayed Sh. M. Al-Issa |
| author_facet | A. M. A. El-Sayed Sh. M. Al-Issa |
| author_sort | A. M. A. El-Sayed |
| collection | DOAJ |
| description | In this paper we present a global existence theorem of a positive monotonic integrable solution for the mixed type nonlinear quadratic integral equation of fractional order\[x(t) = p(t) + h(t,x(t)) \int_{0}^{t} k(t,s)( f_1( s, I^\alpha f_2(s, x(s)))+g_1( s, I^\beta g_2(s, x(s))))ds,~t\in [0,1],\alpha,\beta>0\]by applying the technique of measures of weak noncompactness. As an application, we consider an initial value problem of arbitrary (fractional) order differential equations. |
| first_indexed | 2024-12-24T03:43:37Z |
| format | Article |
| id | doaj.art-fa234e7024fd4dca849bb5e01ea9edff |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-24T03:43:37Z |
| publishDate | 2019-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-fa234e7024fd4dca849bb5e01ea9edff2022-12-21T17:16:48ZengAIMS PressAIMS Mathematics2473-69882019-07-014382183010.3934/math.2019.3.821Monotonic solutions for a quadratic integral equation of fractional orderA. M. A. El-Sayed0Sh. M. Al-Issa11 Faculty of Science, Alexandria University, Alexandria, Egypt2 Faculty of Science, Lebanese International University, Lebanon 3 Faculty of Science, The International University of Beirut, LebanonIn this paper we present a global existence theorem of a positive monotonic integrable solution for the mixed type nonlinear quadratic integral equation of fractional order\[x(t) = p(t) + h(t,x(t)) \int_{0}^{t} k(t,s)( f_1( s, I^\alpha f_2(s, x(s)))+g_1( s, I^\beta g_2(s, x(s))))ds,~t\in [0,1],\alpha,\beta>0\]by applying the technique of measures of weak noncompactness. As an application, we consider an initial value problem of arbitrary (fractional) order differential equations.https://www.aimspress.com/article/10.3934/math.2019.3.821/fulltext.htmlfractional calculusquadratic integral equationfixed point theorymeasure of noncompactness |
| spellingShingle | A. M. A. El-Sayed Sh. M. Al-Issa Monotonic solutions for a quadratic integral equation of fractional order AIMS Mathematics fractional calculus quadratic integral equation fixed point theory measure of noncompactness |
| title | Monotonic solutions for a quadratic integral equation of fractional order |
| title_full | Monotonic solutions for a quadratic integral equation of fractional order |
| title_fullStr | Monotonic solutions for a quadratic integral equation of fractional order |
| title_full_unstemmed | Monotonic solutions for a quadratic integral equation of fractional order |
| title_short | Monotonic solutions for a quadratic integral equation of fractional order |
| title_sort | monotonic solutions for a quadratic integral equation of fractional order |
| topic | fractional calculus quadratic integral equation fixed point theory measure of noncompactness |
| url | https://www.aimspress.com/article/10.3934/math.2019.3.821/fulltext.html |
| work_keys_str_mv | AT amaelsayed monotonicsolutionsforaquadraticintegralequationoffractionalorder AT shmalissa monotonicsolutionsforaquadraticintegralequationoffractionalorder |