Existence and stability of solution for nonlinear differential equations with \(\psi \)-Hilfer fractional derivative. (English) Zbl 1476.45010
Summary: In this paper, we investigate a nonlinear \(\psi \)-Hilfer fractional integro-differential equation on an unbounded domain \([ a , + \infty )\). Firstly, the existence and uniqueness of solution for the equation are proved by means of Banach contraction mapping principle based on suitable growth conditions in an appropriate Banach space. Moreover the stability of Ulam-Hyers-Rassias, Ulam-Hyers and Semi-Ulam-Hyers-Rassias to the initial value problem is obtained.
MSC:
45M10 | Stability theory for integral equations |
26A33 | Fractional derivatives and integrals |
34A08 | Fractional ordinary differential equations |
Keywords:
nonlinear differential equation; \( \psi \)-Hilfer fractional derivative; Banach contraction mapping principleReferences:
[1] | Vanterler da C. Sousa, J.; Capelas de Oliveira, E., On the \(\psi \)-Hilfer fractional derivative, Commun. Nonlinear Sci. Numer. Simul., 60, 72-91 (2018) · Zbl 1470.26015 |
[2] | Ma, Yu-tian; Li, Wen-wen, Application and research of fractional differential equations in dynamic analysis of supply chain financial chaotic system, Chaos Solitons Fractals, 130, Article 109417 pp. (2020) · Zbl 1489.65101 |
[3] | Sun, Hong-guang; Chang, Ai-lian; Zhang, Yong, A survey on the variable-order fractional differential equations: Mathematical foundations, models, numerical methods and its applications, Fract. Calc. Appl. Anal., 22, 27-59 (2019) · Zbl 1428.34001 |
[4] | Kaur, K.; Jindal, N.; Singh, K., Fractional fourier transform based Riesz fractional derivative approach for edge detection and its application in image enhancement, Signal Process., 180, Article 107852 pp. (2021) |
[5] | Shakhmurov, V., Nonlocal fractional differential equations and applications, Complex Anal. Oper. Theory, 14, 4, 1-15 (2020) · Zbl 07229684 |
[6] | Vivek, D.; Kanagarajan, K.; Elsayed, E. M., Some existence and stability results for hilfer-fractional implicit differential equations with nonlocal conditions, Mediterr. J. Math., 15, 1, 15-35 (2018) · Zbl 1390.34029 |
[7] | Zhou, Jue-liang; Zhang, Shu-qin; He, Yu-bo, Existence and stability of solution for a nonlinear fractional differential equation, J. Math. Anal. Appl., 498, 1, Article 124921 pp. (2021) · Zbl 1462.34108 |
[8] | Diaz, J. B.; Margolis, B., A fixed point theorem of the alternative, for contractions on a generalized complete metric space, Bull. Amer. Math. Soc., 74, 305-309 (1968) · Zbl 0157.29904 |
[9] | Vanterler da C. Sousa, J.; Capelas de Oliveira, E., Ulam-Hyers-Rassias stability for a class of fractional integro \(-\) differential equations, Results Math., 73, 3, 111-126 (2018) · Zbl 1401.45011 |
[10] | Cădariu, L.; Găvruţa, L.; Găvruţa, P., Weighted space method for the stability of some nonlinear equations, Appl. Anal. Discrete Math., 6, 1, 126-139 (2012) · Zbl 1289.39054 |
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