On Solvability of Fractional (<i>p</i>,<i>q</i>)-Difference Equations with (<i>p</i>,<i>q</i>)-Difference Anti-Periodic Boundary Conditions
We discuss the solvability of a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow>&l...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/23/4419 |
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| author | Ravi P. Agarwal Hana Al-Hutami Bashir Ahmad |
| author_facet | Ravi P. Agarwal Hana Al-Hutami Bashir Ahmad |
| author_sort | Ravi P. Agarwal |
| collection | DOAJ |
| description | We discuss the solvability of a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-difference equation of fractional order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>α</mi><mo>∈</mo><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>]</mo></mrow></semantics></math></inline-formula>, equipped with anti-periodic boundary conditions involving the first-order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-difference operator. The desired results are accomplished with the aid of standard fixed point theorems. Examples are presented for illustrating the obtained results. |
| first_indexed | 2024-03-09T17:41:03Z |
| format | Article |
| id | doaj.art-d2261ade154e4da0b3e303014c5beb75 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T17:41:03Z |
| publishDate | 2022-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-d2261ade154e4da0b3e303014c5beb752023-11-24T11:33:14ZengMDPI AGMathematics2227-73902022-11-011023441910.3390/math10234419On Solvability of Fractional (<i>p</i>,<i>q</i>)-Difference Equations with (<i>p</i>,<i>q</i>)-Difference Anti-Periodic Boundary ConditionsRavi P. Agarwal0Hana Al-Hutami1Bashir Ahmad2Department of Mathematics, Texas A& M University, Kingsville, TX 78363-8202, USANonlinear Analysis and Applied Mathematics (NAAM)—Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaNonlinear Analysis and Applied Mathematics (NAAM)—Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaWe discuss the solvability of a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-difference equation of fractional order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>α</mi><mo>∈</mo><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>]</mo></mrow></semantics></math></inline-formula>, equipped with anti-periodic boundary conditions involving the first-order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>-difference operator. The desired results are accomplished with the aid of standard fixed point theorems. Examples are presented for illustrating the obtained results.https://www.mdpi.com/2227-7390/10/23/4419fractional Caputo fractional (<i>p</i>,<i>q</i>)-derivative(<i>p</i>,<i>q</i>)-difference operatoranti-periodic boundary conditionsexistencefixed point |
| spellingShingle | Ravi P. Agarwal Hana Al-Hutami Bashir Ahmad On Solvability of Fractional (<i>p</i>,<i>q</i>)-Difference Equations with (<i>p</i>,<i>q</i>)-Difference Anti-Periodic Boundary Conditions Mathematics fractional Caputo fractional (<i>p</i>,<i>q</i>)-derivative (<i>p</i>,<i>q</i>)-difference operator anti-periodic boundary conditions existence fixed point |
| title | On Solvability of Fractional (<i>p</i>,<i>q</i>)-Difference Equations with (<i>p</i>,<i>q</i>)-Difference Anti-Periodic Boundary Conditions |
| title_full | On Solvability of Fractional (<i>p</i>,<i>q</i>)-Difference Equations with (<i>p</i>,<i>q</i>)-Difference Anti-Periodic Boundary Conditions |
| title_fullStr | On Solvability of Fractional (<i>p</i>,<i>q</i>)-Difference Equations with (<i>p</i>,<i>q</i>)-Difference Anti-Periodic Boundary Conditions |
| title_full_unstemmed | On Solvability of Fractional (<i>p</i>,<i>q</i>)-Difference Equations with (<i>p</i>,<i>q</i>)-Difference Anti-Periodic Boundary Conditions |
| title_short | On Solvability of Fractional (<i>p</i>,<i>q</i>)-Difference Equations with (<i>p</i>,<i>q</i>)-Difference Anti-Periodic Boundary Conditions |
| title_sort | on solvability of fractional i p i i q i difference equations with i p i i q i difference anti periodic boundary conditions |
| topic | fractional Caputo fractional (<i>p</i>,<i>q</i>)-derivative (<i>p</i>,<i>q</i>)-difference operator anti-periodic boundary conditions existence fixed point |
| url | https://www.mdpi.com/2227-7390/10/23/4419 |
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