Existence and uniqueness of solution of nonlinear boundary value problems for $\psi$-Caputo fractional differential equations

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Abstract

The aim of the paper is to develop monotone iterative technique and its associated iterative scheme and apply it to prove existence and uniqueness of solution of nonlinear boundary value problem for $\psi$-Caputo fractional differential equation.First we consider initial value problem and choose suitable initial iterations and construct two monotone sequences. It is shown that these two sequences converge monotonically from above and below to maximal and minimal solutions of initial value problem. Further we show that maximal and minimal solutions are quasi solutions of nonlinear boundary value problem for $\psi$-Caputo fractional differential equation which leads to existence and uniqueness of solution of nonlinear boundary value problem for $\psi$-Caputo fractional differential equation.

Keywords:

\psi \text {-Caputo fractional differential equation }, nonlinear boundary conditions, monotone iterative technique, upper lower and quasi solutions, existence uniqueness results

Mathematics Subject Classification:

Mathematics
  • D.B. Dhaigude Emeritus Professor of Mathematics, Marathwada Mathematical Society, Aurangabad-431001, India.
  • V.S. Gore Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad–431004, India.
  • P.D. Kundgar Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad–431004, India.
  • Pages: 112-117
  • Date Published: 01-01-2021
  • Vol. 9 No. 01 (2021): Malaya Journal of Matematik (MJM)

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01-01-2021

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D.B. Dhaigude, V.S. Gore, and P.D. Kundgar. “Existence and Uniqueness of Solution of Nonlinear Boundary Value Problems for $\psi$-Caputo Fractional Differential Equations”. Malaya Journal of Matematik, vol. 9, no. 01, Jan. 2021, pp. 112-7, https://www.malayajournal.org/index.php/mjm/article/view/982.

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Vol. 9 No. 01 (2021): Malaya Journal of Matematik (MJM)

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