ABSTRACT: We investigate a q-fractional integral equation with supremum and prove an existence theorem for it. We will prove that our q-integral equation has a solution in C [0, 1] which is monotonic ...

Lecture notes for an introductory course on the calculus of variations (variational principles). First delivered at SNS, NUST, Pakistan during the spring semester of 2022-23. Currently incomplete.

Lecture Notes-Monograph Series, Vol. 52, Time Series and Related Topics: In Memory of Ching-Zong Wei (2006), pp. 149-164 (16 pages) This paper develops a European option pricing formula for fractional ...

Fractional calculus extends the classical notions of differentiation and integration to non-integer orders, offering an adaptable framework that is particularly well suited to modelling anomalous ...

In this paper, we describe two approaches to the definition of fractional derivatives. We investigate the accuracy of the analysis method for solving the fractional order problem. We also give some ...

Abstract: In this work-in-progress paper, the topic of fractional-order modeling and control in education is discussed. The study of fractional calculus, fractional-order systems (FOS) and the ...

In this paper the whole family of fractional Brownian motions is constructed as a single Gaussian field indexed by time and the Hurst index simultaneously. The field has a simple covariance structure ...

Abstract: Fractional calculus has been adopted in the modelling of many scientific processes and systems. Due to the inherent feature of long term memory of fractional derivatives, it has been used in ...