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Solution of 𝜐 fractional differential equation with non local boundary values via fixed point theory
(UMT Lahore, 2022) Fariha Irshad
Fractional calculus is a meaning of derivative to an integer of any order. The concept of fractional calculus caught the attention of many mathematicians who work on it. Fractional calculus is also known as fractional derivatives. Riemann and Caputo were the famous mathematicians who worked extensively on fractional derivatives. Riemann and Caputo are kinds of fractional derivatives. In 2018, E. Karapinar blended the Kannan fixed point theorem and interpolative theory. The idea was actually the rate of meeting to find fixed point results. In recent years, there have been many developments in finding fixed point results for the contraction used in set-valued mapping with some order. This work is introduced for the study of fractional derivatives of boundary value problems (BVPs), which consist of Riemann–Liouville and Caputo integro-differential equations with multiple nonlinear terms. In this work, we investigate the criteria of existence of solutions for Caputo fractional equations and inclusion problems with nonlocal integral boundary conditions. In order to achieve the solution, we have to use contractive mapping and the theory of endpoints. For each theorem in our work, we provide an example based on the required assumptions to support the new results.