SOME RESULTS ON ψ-CAPUTO FRACTIONAL INTEGRO DIFFERENTIAL EQUATIONS | ||
| Journal of Fractional Calculus and Applications | ||
| Volume 16, Issue 1, 2025, Pages 1-16 PDF (264.6 K) | ||
| Document Type: Regular research papers | ||
| DOI: 10.21608/jfca.2025.319322.1132 | ||
| Authors | ||
| KARTHIKEYAN P* 1; Manikandan A2; vijay D3 | ||
| 1Sri Vasavi College | ||
| 2Department of Mathematics, Government College of Engineering, Erode - 638 316, India | ||
| 3Department of Mathematics,KSR College Arts and Science For Women, Namakkal - 637 215 | ||
| Abstract | ||
| In this article, we discuss the existence and uniqueness of solution for fractional integro differential equation involving ψ- Caputo fractional derivative with boundary conditions. Within the measures of noncompactness , the Kuratowski measure and the Hausdorff measures and out as the most significant. In instance, the Hausdorff measure is widely utilized throughout numerous industries of nonlinear analysis and its related applications. Nonlinear fractional boundary value problems exhibit a broad range of applications in economics, financial mathematics, and other applied sciences. Recently, there has been a theoretical focus on exploring results for fractional differential or integro-differential equations with boundary conditions. Techniques from nonlinear analysis, like the Banach fixed theorem, Leray-Schauder theory, etc., have been employed. The primary analysis is based on the Holder’s inequality, and Monch fixed-point theorem to prove the existence of solutions and establish the sufficient conditions and significance. An example is provided to demonstrate the applicability of finding results. | ||
| Keywords | ||
| fractional differential equations; ψ-Caputo fractional derivative; fractional ψ-integral; boundary value problem; Monch’s fixed point theorem. | ||
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