q-fractional differential equations with uncertainty
In this paper, first we are going to introduce the fuzzy q -derivative and fuzzy q -fractional derivative in Caputo sense by using generalized Hukuhara difference, and then provide the related theorems and properties in detail. Moreover, the characterization theorem between the solutions of fuzzy Ca...
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| Published in | Soft computing (Berlin, Germany) Vol. 23; no. 19; pp. 9507 - 9524 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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Berlin/Heidelberg
Springer Berlin Heidelberg
01.10.2019
Springer Nature B.V |
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| Abstract | In this paper, first we are going to introduce the fuzzy
q
-derivative and fuzzy
q
-fractional derivative in Caputo sense by using generalized Hukuhara difference, and then provide the related theorems and properties in detail. Moreover, the characterization theorem between the solutions of fuzzy Caputo
q
-fractional initial value problem (for short FCqF-IVP), which allows us to translate a FCqF-IVP and system of ordinary Caputo
q
-fractional differential equations (for short OCqF-DEs), is presented. In detail, the existence and uniqueness theorem is proved for the solution of FCqF-IVP. Finally, we restrict our attention to explain our idea for solving the FCqF-IVP and introducing its numerical solution by means of
q
-Mittag-Leffler function. The numerical examples demonstrate that the proposed idea is quite reasonable. |
|---|---|
| AbstractList | In this paper, first we are going to introduce the fuzzy
q
-derivative and fuzzy
q
-fractional derivative in Caputo sense by using generalized Hukuhara difference, and then provide the related theorems and properties in detail. Moreover, the characterization theorem between the solutions of fuzzy Caputo
q
-fractional initial value problem (for short FCqF-IVP), which allows us to translate a FCqF-IVP and system of ordinary Caputo
q
-fractional differential equations (for short OCqF-DEs), is presented. In detail, the existence and uniqueness theorem is proved for the solution of FCqF-IVP. Finally, we restrict our attention to explain our idea for solving the FCqF-IVP and introducing its numerical solution by means of
q
-Mittag-Leffler function. The numerical examples demonstrate that the proposed idea is quite reasonable. In this paper, first we are going to introduce the fuzzy q-derivative and fuzzy q-fractional derivative in Caputo sense by using generalized Hukuhara difference, and then provide the related theorems and properties in detail. Moreover, the characterization theorem between the solutions of fuzzy Caputo q-fractional initial value problem (for short FCqF-IVP), which allows us to translate a FCqF-IVP and system of ordinary Caputo q-fractional differential equations (for short OCqF-DEs), is presented. In detail, the existence and uniqueness theorem is proved for the solution of FCqF-IVP. Finally, we restrict our attention to explain our idea for solving the FCqF-IVP and introducing its numerical solution by means of q-Mittag-Leffler function. The numerical examples demonstrate that the proposed idea is quite reasonable. |
| Author | Allahviranloo, T. Noeiaghdam, Z. Nieto, Juan J. |
| Author_xml | – sequence: 1 givenname: Z. surname: Noeiaghdam fullname: Noeiaghdam, Z. email: Z_Noeiaghdam@shahed.ac.ir organization: Department of Mathematics and Computer Science, Shahed University – sequence: 2 givenname: T. surname: Allahviranloo fullname: Allahviranloo, T. organization: Faculty of Engineering and Natural Sciences, Bahcesehir University – sequence: 3 givenname: Juan J. surname: Nieto fullname: Nieto, Juan J. organization: Departamento de Estatística, Analise Matemática e Optimización, Instituto de Matemáticas, Universidade de Santiago de Compostela |
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| Cites_doi | 10.1016/j.aml.2015.02.013 10.1016/S0165-0114(96)00270-9 10.1016/j.na.2009.02.008 10.1016/j.cnsns.2012.06.016 10.1038/nphys3941 10.2298/AADM0701311R 10.1016/j.nahs.2009.06.010 10.1017/S0080456800002751 10.1016/j.cnsns.2011.01.026 10.1016/j.fss.2012.10.003 10.1007/978-3-642-05014-5 10.1016/S0165-0114(97)00310-2 10.1016/j.jfranklin.2014.01.020 10.1016/j.ins.2007.11.016 10.1016/0022-247X(86)90093-4 10.1515/IJNSNS.2006.7.1.27 10.1017/S0013091500011469 10.1007/s12190-014-0784-3 10.1016/j.na.2009.11.029 10.1016/j.fss.2004.08.001 10.1016/j.cam.2017.09.039 10.2478/s13540-014-0155-7 10.1017/S0305004100045060 10.1016/j.nonrwa.2012.08.001 10.1016/j.aml.2016.01.003 10.3846/13926292.2013.760012 10.1016/j.na.2008.12.005 10.1016/j.cnsns.2014.12.014 10.3233/IFS-130831 |
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| Keywords | Generalized Hukuhara difference Mittag-Leffler function fractional derivative derivative fractional initial value problems Fuzzy Krasnoselskii–Krein-type conditions Fuzzy Caputo |
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| Snippet | In this paper, first we are going to introduce the fuzzy
q
-derivative and fuzzy
q
-fractional derivative in Caputo sense by using generalized Hukuhara... In this paper, first we are going to introduce the fuzzy q-derivative and fuzzy q-fractional derivative in Caputo sense by using generalized Hukuhara... |
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| SubjectTerms | Approximation Artificial Intelligence Boundary value problems Calculus Computational Intelligence Control Derivatives Differential equations Engineering Existence theorems Foundations Fractional calculus Mathematical functions Mathematical Logic and Foundations Mechatronics Robotics Uniqueness theorems |
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| Title | q-fractional differential equations with uncertainty |
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