Positive solution of a fractional differential equation with integral boundary conditions

• Autorzy: Abdo M. S. , Wahash H. A. , Panchal S. K.

Identyfikatory

DOI

10.17512/jamcm.2018.3.01

• Języki publikacji: EN

Abstrakty

EN

In this paper, we prove the existence and uniqueness of a positive solution for a boundary value problem of nonlinear fractional differential equations involving a Caputo fractional operator with integral boundary conditions. The technique used to prove our results depends on the upper and lower solution, the Schauder fixed point theorem and the Banach contraction principle. The result of existence obtained through constructing the upper and lower control functions of the nonlinear term without any monotone requirement.

Słowa kluczowe

EN

fractional derivative and integral; positive solutions of nonlinear boundary value problems; upper and lower solutions; fixed point theorem

PL

pochodna ułamkowa; twierdzenie o punkcie stałym; twierdzenia o punkcie stałym Schaudera; równania różniczkowe cząstkowe; nieliniowe cząstkowe równanie różniczkowe; zagadnienie brzegowe

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2018
• Tom: Vol. 17, nr 3
• Strony: 5--15
• Opis fizyczny: Bibliogr. 20 poz.

Twórcy

autor

Abdo M. S.

• Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University Aurangabad 431004 (M.S.), India
• Department of Mathematics, Hodeidah University Al-Hodeidah, Yemen

autor

Wahash H. A.

• Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University Aurangabad 431004 (M.S.), India

autor

Panchal S. K.

• Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University Aurangabad 431004 (M.S.), India

Bibliografia

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• [3] Miller, K.S.,& Ross, B. (1993). An Introduction to the Fractional Calculus and Differential Equations. New York: John Wiley.
• [4] Podlubny, I. (1999). Fractional Differential Equations. San Diego: Academic Press.
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• [18] Nanware, J.A., & Dhaigude, D.B. (2014). Existence and uniqueness of solutions of differential equations of fractional order with integral boundary conditions. Journal of Nonlinear Sciences and Applications, 7(4), 246-254.
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Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).