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Nonlinear singular $ p $ -Laplacian boundary value problems in the frame of conformable derivative
On the fuzzy stability results for fractional stochastic Volterra integral equation
| a. | School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran |
| b. | Institute for Groundwater Studies (IGS) Faculty: Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9300, South Africa |
By a fuzzy controller function, we stable a random operator associated with a type of fractional stochastic Volterra integral equations. Using the fixed point technique, we get an approximation for the mentioned random operator by a solution of the fractional stochastic Volterra integral equation.
References:
| [1] |
R. P. Agarwal, R. Saadati and A. Salamati, Approximation of the multiplicatives on random multi-normed space, Journal of inequalities and applications, 204 (2017), 204.
doi: 10.1186/s13660-017-1478-9. |
| [2] |
T. Bag and S. K. Samanta,
Finite dimensional intuitionistic fuzzy normed linear spaces, Ann. Fuzzy Math. Inform, 6 (2013), 45-57.
|
| [3] |
Y. J. Cho, T. M. Rassias and R. Saadati, Stability of functional equations in random normed spaces, Springer Optimization and Its Applications, 86, Springer, New York, 2013.
doi: 10.1007/978-1-4614-8477-6. |
| [4] |
C. D. Constantinescu, J. M. Ramirez and W. R. Zhu,
An application of fractional differential equations to risk theory, Finance and Stochastics, 23 (2019), 1001-1024.
doi: 10.1007/s00780-019-00400-8. |
| [5] |
L. Cădariu and V. Radu, Fixed points and the stability of Jensen's functional equation, J. Inequal. Pure Appl. Math, 4 (2003), 4. |
| [6] |
J. B. Diaz and B. Margolis,
A fixed point theorem of the alternative, for contractions on a generalized complete metric space, Bulletin of the American Mathematical Society, 74 (1968), 305-309.
doi: 10.1090/S0002-9904-1968-11933-0. |
| [7] |
M. A. El-Moneam, F. Tarek Ibrahim and S. Elamody,
Stability of a fractional difference equation of high order, Journal of Nonlinear Sciences and Applications, 12 (2019), 65-74.
doi: 10.22436/jnsa.012.02.01. |
| [8] |
A. M. A. El-Sayed and F.M. Gaafar, Positive solutions of singular Hadamard-type fractional differential equations with infinite-point boundary conditions or integral boundary conditions, Advances in Difference Equations, 2019 (2019), 382.
doi: 10.1186/s13662-019-2315-x. |
| [9] |
O. Hadžić and E. Pap, Fixed Point Theory in Probabilistic Metric Spaces, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2001.
doi: 10.1007/978-94-017-1560-7. |
| [10] |
J. Jiang, D. O'Regan, J. Xu and Z. Fu,
Positive solutions for a system of nonlinear Hadamard fractional differential equations involving coupled integral boundary conditions, Journal of Inequalities and Applications, 2019 (2019), 1-18.
doi: 10.1186/s13660-019-2156-x. |
| [11] |
S. Jung, A fixed point approach to the stability of differential equations $y^{'} = F (x, y)$, Bulletin of the Malaysian Mathematical Sciences Society, 33 (2010). |
| [12] |
S. M. Jung, A fixed point approach to the stability of an integral equation related to the wave equation, in Abstract and Applied Analysis, 2013, Hindawi, 2013.
doi: 10.1155/2013/612576. |
| [13] |
H. Khan, T. Abdeljawad, M. Aslam, R. A. Khan and A. Khan,
Existence of positive solution and Hyers–Ulam stability for a nonlinear singular-delay-fractional differential equation, Advances in Difference Equations, 2019 (2019), 1-13.
doi: 10.1186/s13662-019-2054-z. |
| [14] |
H. Khan, F. Jarad, T. Abdeljawad and A. Khan,
A singular ABC-fractional differential equation with $p$-Laplacian operator, Chaos, Solitons & Fractals, 129 (2019), 56-61.
doi: 10.1016/j.chaos.2019.08.017. |
| [15] |
H. Khan, A. Khan, T. Abdeljawad and A. Alkhazzan, Existence results in Banach space for a nonlinear impulsive system, Advances in Difference Equations, 2019 (2019), 18.
doi: 10.1186/s13662-019-1965-z. |
| [16] |
A. Khan, H. Khan, J. F. Gómez-Aguilar and T. Abdeljawad,
Existence and Hyers-Ulam stability for a nonlinear singular fractional differential equations with Mittag-Leffler kernel, Chaos, Solitons & Fractals, 127 (2019), 422-427.
doi: 10.1016/j.chaos.2019.07.026. |
| [17] |
H. Khan, A. Khan, F. Jarad and A. Shah, Existence and data dependence theorems for solutions of an ABC-fractional order impulsive system, Chaos, Solitons & Fractals, (2019), 109477.
doi: 10.1016/j.chaos.2019.109477. |
| [18] |
Y. Ma and W. Li, Application and research of fractional differential equations in dynamic analysis of supply chain financial chaotic system, Chaos, Solitons & Fractals, 130 (2020), 109417.
doi: 10.1016/j.chaos.2019.109417. |
| [19] |
D. Miheţ and V. Radu,
On the stability of the additive Cauchy functional equation in random normed spaces, Journal of mathematical Analysis and Applications, 343 (2008), 567-572.
doi: 10.1016/j.jmaa.2008.01.100. |
| [20] |
D. Miheţ and R. Saadati,
On the stability of the additive Cauchy functional equation in random normed spaces, Applied mathematics letters, 24 (2011), 2005-2009.
doi: 10.1016/j.aml.2011.05.033. |
| [21] |
A. K. Mirmostafaee,
Perturbation of generalized derivations in fuzzy Menger normed algebras, Fuzzy sets and systems, 195 (2012), 109-117.
doi: 10.1016/j.fss.2011.10.015. |
| [22] |
H. K. Nashine and R. W. Ibrahim,
Symmetric solutions of nonlinear fractional integral equations via a new fixed point theorem under FG-contractive condition, Numerical Functional Analysis and Optimization, 40 (2019), 1448-1466.
doi: 10.1080/01630563.2019.1602779. |
| [23] |
S. Nadaban, T. Binzar and F. Pater,
Some fixed point theorems for $\varphi$-contractive mappings in fuzzy normed linear spaces, Journal of Nonlinear Sciences and Applications, 10 (2017), 5668-5676.
doi: 10.22436/jnsa.010.11.05. |
| [24] |
R. Naeem and M. Anwar,
Jessen type functionals and exponential convexity, J. Math. Comput. Sci, 17 (2017), 429-436.
doi: 10.22436/jmcs.017.03.08. |
| [25] |
R. Naeem and M. Anwar,
Weighted Jessen's functionals and exponential convexity, J. Math. Comput. Sci, 19 (2019), 171-180.
doi: 10.22436/jmcs.019.03.04. |
| [26] |
C. Park, D. Y. Shin, R. Saadati and J. R. Lee,
A fixed point approach to the fuzzy stability of an AQCQ-functional equation, Filomat, 30 (2016), 1833-1851.
doi: 10.2298/FIL1607833P. |
| [27] |
C. Park, S. O. Kim and C. Alaca,
Stability of additive-quadratic rho-functional equations in Banach spaces: A fixed point approach, J. Nonlin. Sci. Appl., 10 (2017), 1252-1262.
doi: 10.22436/jnsa.010.03.34. |
| [28] |
G. Sadeghi, M. Nazarianpoor and J. M. Rassias,
Solution and stability of quattuorvigintic functional equation in intuitionistic fuzzy normed spaces, Iranian Journal of Fuzzy Systems, 15 (2018), 13-30.
|
| [29] |
R. Saadati and S. M. Vaezpour,
Some results on fuzzy Banach spaces, Journal of Applied Mathematics and Computing, 17 (2005), 475-484.
doi: 10.1007/BF02936069. |
| [30] |
R. Saadati and C. Park,
Approximation of derivations and the superstability in random Banach $\ast$-algebras, Advances in Difference Equations, 2018 (2018), 1-12.
doi: 10.1186/s13662-018-1882-6. |
| [31] |
W. Wei, X. Li and X. Li,
New stability results for fractional integral equation, Computers & Mathematics with Applications, 64 (2012), 3468-3476.
doi: 10.1016/j.camwa.2012.02.057. |
show all references
References:
| [1] |
R. P. Agarwal, R. Saadati and A. Salamati, Approximation of the multiplicatives on random multi-normed space, Journal of inequalities and applications, 204 (2017), 204.
doi: 10.1186/s13660-017-1478-9. |
| [2] |
T. Bag and S. K. Samanta,
Finite dimensional intuitionistic fuzzy normed linear spaces, Ann. Fuzzy Math. Inform, 6 (2013), 45-57.
|
| [3] |
Y. J. Cho, T. M. Rassias and R. Saadati, Stability of functional equations in random normed spaces, Springer Optimization and Its Applications, 86, Springer, New York, 2013.
doi: 10.1007/978-1-4614-8477-6. |
| [4] |
C. D. Constantinescu, J. M. Ramirez and W. R. Zhu,
An application of fractional differential equations to risk theory, Finance and Stochastics, 23 (2019), 1001-1024.
doi: 10.1007/s00780-019-00400-8. |
| [5] |
L. Cădariu and V. Radu, Fixed points and the stability of Jensen's functional equation, J. Inequal. Pure Appl. Math, 4 (2003), 4. |
| [6] |
J. B. Diaz and B. Margolis,
A fixed point theorem of the alternative, for contractions on a generalized complete metric space, Bulletin of the American Mathematical Society, 74 (1968), 305-309.
doi: 10.1090/S0002-9904-1968-11933-0. |
| [7] |
M. A. El-Moneam, F. Tarek Ibrahim and S. Elamody,
Stability of a fractional difference equation of high order, Journal of Nonlinear Sciences and Applications, 12 (2019), 65-74.
doi: 10.22436/jnsa.012.02.01. |
| [8] |
A. M. A. El-Sayed and F.M. Gaafar, Positive solutions of singular Hadamard-type fractional differential equations with infinite-point boundary conditions or integral boundary conditions, Advances in Difference Equations, 2019 (2019), 382.
doi: 10.1186/s13662-019-2315-x. |
| [9] |
O. Hadžić and E. Pap, Fixed Point Theory in Probabilistic Metric Spaces, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2001.
doi: 10.1007/978-94-017-1560-7. |
| [10] |
J. Jiang, D. O'Regan, J. Xu and Z. Fu,
Positive solutions for a system of nonlinear Hadamard fractional differential equations involving coupled integral boundary conditions, Journal of Inequalities and Applications, 2019 (2019), 1-18.
doi: 10.1186/s13660-019-2156-x. |
| [11] |
S. Jung, A fixed point approach to the stability of differential equations $y^{'} = F (x, y)$, Bulletin of the Malaysian Mathematical Sciences Society, 33 (2010). |
| [12] |
S. M. Jung, A fixed point approach to the stability of an integral equation related to the wave equation, in Abstract and Applied Analysis, 2013, Hindawi, 2013.
doi: 10.1155/2013/612576. |
| [13] |
H. Khan, T. Abdeljawad, M. Aslam, R. A. Khan and A. Khan,
Existence of positive solution and Hyers–Ulam stability for a nonlinear singular-delay-fractional differential equation, Advances in Difference Equations, 2019 (2019), 1-13.
doi: 10.1186/s13662-019-2054-z. |
| [14] |
H. Khan, F. Jarad, T. Abdeljawad and A. Khan,
A singular ABC-fractional differential equation with $p$-Laplacian operator, Chaos, Solitons & Fractals, 129 (2019), 56-61.
doi: 10.1016/j.chaos.2019.08.017. |
| [15] |
H. Khan, A. Khan, T. Abdeljawad and A. Alkhazzan, Existence results in Banach space for a nonlinear impulsive system, Advances in Difference Equations, 2019 (2019), 18.
doi: 10.1186/s13662-019-1965-z. |
| [16] |
A. Khan, H. Khan, J. F. Gómez-Aguilar and T. Abdeljawad,
Existence and Hyers-Ulam stability for a nonlinear singular fractional differential equations with Mittag-Leffler kernel, Chaos, Solitons & Fractals, 127 (2019), 422-427.
doi: 10.1016/j.chaos.2019.07.026. |
| [17] |
H. Khan, A. Khan, F. Jarad and A. Shah, Existence and data dependence theorems for solutions of an ABC-fractional order impulsive system, Chaos, Solitons & Fractals, (2019), 109477.
doi: 10.1016/j.chaos.2019.109477. |
| [18] |
Y. Ma and W. Li, Application and research of fractional differential equations in dynamic analysis of supply chain financial chaotic system, Chaos, Solitons & Fractals, 130 (2020), 109417.
doi: 10.1016/j.chaos.2019.109417. |
| [19] |
D. Miheţ and V. Radu,
On the stability of the additive Cauchy functional equation in random normed spaces, Journal of mathematical Analysis and Applications, 343 (2008), 567-572.
doi: 10.1016/j.jmaa.2008.01.100. |
| [20] |
D. Miheţ and R. Saadati,
On the stability of the additive Cauchy functional equation in random normed spaces, Applied mathematics letters, 24 (2011), 2005-2009.
doi: 10.1016/j.aml.2011.05.033. |
| [21] |
A. K. Mirmostafaee,
Perturbation of generalized derivations in fuzzy Menger normed algebras, Fuzzy sets and systems, 195 (2012), 109-117.
doi: 10.1016/j.fss.2011.10.015. |
| [22] |
H. K. Nashine and R. W. Ibrahim,
Symmetric solutions of nonlinear fractional integral equations via a new fixed point theorem under FG-contractive condition, Numerical Functional Analysis and Optimization, 40 (2019), 1448-1466.
doi: 10.1080/01630563.2019.1602779. |
| [23] |
S. Nadaban, T. Binzar and F. Pater,
Some fixed point theorems for $\varphi$-contractive mappings in fuzzy normed linear spaces, Journal of Nonlinear Sciences and Applications, 10 (2017), 5668-5676.
doi: 10.22436/jnsa.010.11.05. |
| [24] |
R. Naeem and M. Anwar,
Jessen type functionals and exponential convexity, J. Math. Comput. Sci, 17 (2017), 429-436.
doi: 10.22436/jmcs.017.03.08. |
| [25] |
R. Naeem and M. Anwar,
Weighted Jessen's functionals and exponential convexity, J. Math. Comput. Sci, 19 (2019), 171-180.
doi: 10.22436/jmcs.019.03.04. |
| [26] |
C. Park, D. Y. Shin, R. Saadati and J. R. Lee,
A fixed point approach to the fuzzy stability of an AQCQ-functional equation, Filomat, 30 (2016), 1833-1851.
doi: 10.2298/FIL1607833P. |
| [27] |
C. Park, S. O. Kim and C. Alaca,
Stability of additive-quadratic rho-functional equations in Banach spaces: A fixed point approach, J. Nonlin. Sci. Appl., 10 (2017), 1252-1262.
doi: 10.22436/jnsa.010.03.34. |
| [28] |
G. Sadeghi, M. Nazarianpoor and J. M. Rassias,
Solution and stability of quattuorvigintic functional equation in intuitionistic fuzzy normed spaces, Iranian Journal of Fuzzy Systems, 15 (2018), 13-30.
|
| [29] |
R. Saadati and S. M. Vaezpour,
Some results on fuzzy Banach spaces, Journal of Applied Mathematics and Computing, 17 (2005), 475-484.
doi: 10.1007/BF02936069. |
| [30] |
R. Saadati and C. Park,
Approximation of derivations and the superstability in random Banach $\ast$-algebras, Advances in Difference Equations, 2018 (2018), 1-12.
doi: 10.1186/s13662-018-1882-6. |
| [31] |
W. Wei, X. Li and X. Li,
New stability results for fractional integral equation, Computers & Mathematics with Applications, 64 (2012), 3468-3476.
doi: 10.1016/j.camwa.2012.02.057. |
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